[Cohomologie locale et support pour les catégories triangulées]
Nous proposons une façon nouvelle de définir une notion de support pour les objets d'une catégorie avec petits coproduits, engendrée par des objets compacts. Cette approche est basée sur une construction des foncteurs de cohomologie locale sur les catégories triangulées relativement à un anneau central d'opérateurs. Comme cas particuliers, on retrouve la théorie pour les anneaux noethériens de Foxby et Neeman, la théorie d'Avramov et Buchweitz pour les anneaux locaux d'intersection complète, ou les variétés pour les représentations des groupes finis selon Benson, Carlson et Rickard. Nous donnons des exemples explicites d'objets dont le support triangulé et le support cohomologique diffèrent. Dans le cas des représentations des groupes, ceci nous permet de corriger et d'établir une conjecture de Benson.
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Special cases are, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects, the triangulated support and cohomological support of which differ. In the case of group representations, this allows us to correct and establish a conjecture of Benson.
@article{ASENS_2008_4_41_4_575_0, author = {Benson, Dave and Iyengar, Srikanth B. and Krause, Henning}, title = {Local cohomology and support for triangulated categories}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {575--621}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 41}, number = {4}, year = {2008}, doi = {10.24033/asens.2076}, mrnumber = {2489634}, zbl = {1171.18007}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.2076/} }
TY - JOUR AU - Benson, Dave AU - Iyengar, Srikanth B. AU - Krause, Henning TI - Local cohomology and support for triangulated categories JO - Annales scientifiques de l'École Normale Supérieure PY - 2008 SP - 575 EP - 621 VL - 41 IS - 4 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/asens.2076/ DO - 10.24033/asens.2076 LA - en ID - ASENS_2008_4_41_4_575_0 ER -
%0 Journal Article %A Benson, Dave %A Iyengar, Srikanth B. %A Krause, Henning %T Local cohomology and support for triangulated categories %J Annales scientifiques de l'École Normale Supérieure %D 2008 %P 575-621 %V 41 %N 4 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/asens.2076/ %R 10.24033/asens.2076 %G en %F ASENS_2008_4_41_4_575_0
Benson, Dave; Iyengar, Srikanth B.; Krause, Henning. Local cohomology and support for triangulated categories. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 41 (2008) no. 4, pp. 575-621. doi : 10.24033/asens.2076. http://archive.numdam.org/articles/10.24033/asens.2076/
[1] Localization in categories of complexes and unbounded resolutions, Canad. J. Math. 52 (2000), 225-247. | Zbl
, & ,[2] Bousfield localization on formal schemes, J. Algebra 278 (2004), 585-610. | Zbl
, & ,[3] Modules of finite virtual projective dimension, Invent. Math. 96 (1989), 71-101. | MR | Zbl
,[4] Infinite free resolutions, in Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math. 166, Birkhäuser, 1998, 1-118. | MR | Zbl
,[5] Homological algebra modulo a regular sequence with special attention to codimension two, J. Algebra 230 (2000), 24-67. | Zbl
& ,[6] Support varieties and cohomology over complete intersections, Invent. Math. 142 (2000), 285-318. | Zbl
& ,[7] Differential graded homological algebra, in preparation.
, & ,[8] Complete intersection dimension, Publ. Math. I.H.É.S. 86 (1997), 67-114. | Numdam | Zbl
, & ,[9] Constructing modules with prescribed cohomological support, Illinois J. Math. 51 (2007), 1-20. | Zbl
& ,[10] Cohomology operators defined by a deformation, J. Algebra 204 (1998), 684-710. | Zbl
& ,[11] Supports and filtrations in algebraic geometry and modular representation theory, Amer. J. Math. 129 (2007), 1227-1250. | MR | Zbl
,[12] Faisceaux pervers, in Analysis and topology on singular spaces, I (Luminy, 1981), Astérisque 100, Soc. Math. France, 1982, 5-171. | MR | Zbl
, & ,[13] Representations and cohomology. II, Cambridge Studies in Advanced Mathematics 31, Cambridge University Press, 1991. | MR | Zbl
,[14] Commutative algebra in the cohomology of groups, in Trends in commutative algebra, Math. Sci. Res. Inst. Publ. 51, Cambridge Univ. Press, 2004, 1-50. | MR | Zbl
,[15] Varieties and cohomology of infinitely generated modules, Arch. Math. (Basel) 91 (2008), 122-125. | Zbl
& ,[16] Complexity and varieties for infinitely generated modules. II, Math. Proc. Cambridge Philos. Soc. 120 (1996), 597-615. | Zbl
, & ,[17] Stratifying modular representations of finite groups, preprint, 2008. | Zbl
, & ,[18] Pure injectives and the spectrum of the cohomology ring of a finite group, J. reine angew. Math. 542 (2002), 23-51. | Zbl
& ,
[19] Complexes of injective
[20] On support varieties for modules over complete intersections, Proc. Amer. Math. Soc. 135 (2007), 3795-3803. | MR | Zbl
,[21] Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, 1993. | Zbl
& ,[22] The varieties and the cohomology ring of a module, J. Algebra 85 (1983), 104-143. | MR | Zbl
,[23] The variety of an indecomposable module is connected, Invent. Math. 77 (1984), 291-299. | MR | Zbl
,[24] Homological algebra, Princeton University Press, 1956. | Zbl
& ,[25] Krull-Schmidt decompositions for thick subcategories, J. Pure Appl. Algebra 210 (2007), 11-27. | MR | Zbl
,
[26] Support varieties for selfinjective algebras,
[27] Bounded complexes of flat modules, J. Pure Appl. Algebra 15 (1979), 149-172. | MR | Zbl
,[28] Depth and amplitude for unbounded complexes, in Commutative algebra (Grenoble / Lyon, 2001), Contemp. Math. 331, Amer. Math. Soc., 2003, 119-137. | Zbl
& ,
[29]
[30] Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer New York, Inc., New York, 1967. | Zbl
& ,
[31] Derived functors of
[32] Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), Documents mathématiques, 4, Soc. Math. France, 2005, Séminaire de Géométrie Algébrique du Bois Marie, 1962. | MR | Zbl
,[33] A change of ring theorem with applications to Poincaré series and intersection multiplicity, Math. Scand. 34 (1974), 167-183. | MR | Zbl
,[34] Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. Lecture Notes in Math., No. 20, Springer, 1966. | MR
,[35] Global methods in homotopy theory, in Homotopy theory (Durham, 1985), London Math. Soc. Lecture Note Ser. 117, Cambridge Univ. Press, 1987, 73-96. | MR | Zbl
,[36] Axiomatic stable homotopy theory, Mem. Amer. Math. Soc. 128 (1997), 114. | Zbl
, & ,[37] Acyclicity versus total acyclicity for complexes over Noetherian rings, Doc. Math. 11 (2006), 207-240. | Zbl
& ,[38] Decomposing thick subcategories of the stable module category, Math. Ann. 313 (1999), 95-108. | MR | Zbl
,[39] A Brown representability theorem via coherent functors, Topology 41 (2002), 853-861. | MR | Zbl
,[40] The stable derived category of a Noetherian scheme, Compos. Math. 141 (2005), 1128-1162. | MR | Zbl
,[41] Thick subcategories of modules over commutative Noetherian rings, Math. Ann. 340 (2008), 733-747. | MR | Zbl
,[42] Equivariant stable homotopy theory, Lecture Notes in Math. 1213, Springer, 1986. | Zbl
, , & ,[43] Lectures on local cohomology and duality, in Local cohomology and its applications (Guanajuato, 1999), Lecture Notes in Pure and Appl. Math. 226, Dekker, 2002, 39-89. | MR | Zbl
,[44] Categories for the working mathematician, Graduate Texts in Math. 5, Springer, 1971. | MR | Zbl
,[45] Spectra and the Steenrod algebra, North-Holland Mathematical Library 29, North-Holland Publishing Co., 1983. | MR | Zbl
,[46] Commutative ring theory, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, 1986. | MR | Zbl
,
[47] The chromatic tower for
[48] Triangulated categories, Annals of Mathematics Studies 148, Princeton University Press, 2001. | MR | Zbl
,[49] The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. 94 (1971), 549-572; ibid. 94 (1971), 573-602. | MR | Zbl
,[50] Idempotent modules in the stable category, J. London Math. Soc. 56 (1997), 149-170. | MR | Zbl
,[51] Cohomologie des algèbres associatives, Ann. Sci. École Norm. Sup. 78 (1961), 163-209. | Numdam | MR | Zbl
,[52] Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (2004), 705-732. | Zbl
& ,[53] Support varieties for modules and complexes, in Trends in representation theory of algebras and related topics, Contemp. Math. 406, Amer. Math. Soc., 2006, 239-270. | MR | Zbl
,[54] The classification of triangulated subcategories, Compositio Math. 105 (1997), 1-27. | MR | Zbl
,- Balmer spectra and Drinfeld centers, Algebra Number Theory, Volume 18 (2024) no. 6, pp. 1081-1116 | DOI:10.2140/ant.2024.18.1081 | Zbl:7844340
- Fibrewise stratification of group representations, Annals of Representation Theory, Volume 1 (2024) no. 1, pp. 97-124 | DOI:10.5802/art.6 | Zbl:7888042
- Cosupport for tensor triangulated categories, Bulletin of the Iranian Mathematical Society, Volume 50 (2024) no. 4, p. 22 (Id/No 50) | DOI:10.1007/s41980-024-00892-x | Zbl:7948572
- Introduction, Categorical Donaldson-Thomas Theory for Local Surfaces, Volume 2350 (2024), p. 1 | DOI:10.1007/978-3-031-61705-8_1
- Koszul Duality Equivalence, Categorical Donaldson-Thomas Theory for Local Surfaces, Volume 2350 (2024), p. 41 | DOI:10.1007/978-3-031-61705-8_2
- Cosupport for compactly generated triangulated categories, Journal of the Australian Mathematical Society, Volume 116 (2024) no. 1, pp. 128-144 | DOI:10.1017/s1446788722000222 | Zbl:1530.13029
- Local (Co)homology and Čech (Co)complexes with Respect to a Pair of Ideals, Mathematics, Volume 12 (2024) no. 3, p. 437 | DOI:10.3390/math12030437
- Categorical properties of reduction functors over non-positive DG-rings, Proceedings of the American Mathematical Society, Volume 152 (2024) no. 2, pp. 489-500 | DOI:10.1090/proc/16517 | Zbl:7783123
- Bounds on cohomological support varieties, Transactions of the American Mathematical Society. Series B, Volume 11 (2024), pp. 703-726 | DOI:10.1090/btran/182 | Zbl:1544.13019
- Local dualisable objects in local algebra, Triangulated categories in representation theory and beyond. The Abel symposium 2022, Ålesund, Norway, June 6–10, 2022, Cham: Springer, 2024, pp. 85-103 | DOI:10.1007/978-3-031-57789-5_3 | Zbl:7950524
- Support theory for Drinfeld doubles of some infinitesimal group schemes, Algebra Number Theory, Volume 17 (2023) no. 1, pp. 217-260 | DOI:10.2140/ant.2023.17.217 | Zbl:1521.16021
- Hypersurface support and prime ideal spectra for stable categories, Annals of
-Theory, Volume 8 (2023) no. 1, pp. 25-79 | DOI:10.2140/akt.2023.8.25 | Zbl:1523.16040 - Stratification in tensor triangular geometry with applications to spectral Mackey functors, Cambridge Journal of Mathematics, Volume 11 (2023) no. 4, pp. 829-915 | DOI:10.4310/cjm.2023.v11.n4.a2 | Zbl:1524.18032
- On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov, Compositio Mathematica, Volume 159 (2023) no. 3, pp. 437-487 | DOI:10.1112/s0010437x22007886 | Zbl:1541.14054
- Another version of cosupport in
., Czechoslovak Mathematical Journal, Volume 73 (2023) no. 2, pp. 431-452 | DOI:10.21136/cmj.2023.0282-21 | Zbl:7729516 - Support for Integrable Hopf Algebras via Noncommutative Hypersurfaces, International Mathematics Research Notices, Volume 2023 (2023) no. 3, p. 1882 | DOI:10.1093/imrn/rnab264
- Local Gorenstein duality in chromatic group cohomology, Journal of Pure and Applied Algebra, Volume 227 (2023) no. 11, p. 29 (Id/No 107422) | DOI:10.1016/j.jpaa.2023.107422 | Zbl:1522.55010
- Cohomological jump loci and duality in local algebra, Mathematische Zeitschrift, Volume 304 (2023) no. 2, p. 18 (Id/No 30) | DOI:10.1007/s00209-023-03276-9 | Zbl:1523.13025
- Stratification and the smashing spectrum, Mathematische Zeitschrift, Volume 305 (2023) no. 4, p. 27 (Id/No 54) | DOI:10.1007/s00209-023-03378-4 | Zbl:1524.18026
- Dirac Geometry I: Commutative Algebra, Peking Mathematical Journal (2023) | DOI:10.1007/s42543-023-00072-6
- Torsion models for tensor-triangulated categories: the one-step case, Algebraic Geometric Topology, Volume 22 (2022) no. 6, pp. 2805-2856 | DOI:10.2140/agt.2022.22.2805 | Zbl:1511.55013
- On stratification for spaces with Noetherian mod
cohomology, American Journal of Mathematics, Volume 144 (2022) no. 4, pp. 895-941 | DOI:10.1353/ajm.2022.0019 | Zbl:1505.55022 - Cohomological supports of tensor products of modules over commutative rings, Research in the Mathematical Sciences, Volume 9 (2022) no. 2, p. 15 (Id/No 25) | DOI:10.1007/s40687-022-00321-7 | Zbl:1493.13021
- On conjectures of Hovey-Strickland and Chai, Selecta Mathematica. New Series, Volume 28 (2022) no. 3, p. 31 (Id/No 56) | DOI:10.1007/s00029-022-00766-2 | Zbl:1515.14054
- Adic Foxby classes, Algebras and Representation Theory, Volume 24 (2021) no. 5, pp. 1155-1189 | DOI:10.1007/s10468-020-09984-8 | Zbl:1477.13024
- Depth and dimension for triangulated categories, Bulletin of the Iranian Mathematical Society, Volume 47 (2021), pp. 143-157 | DOI:10.1007/s41980-021-00607-6 | Zbl:1476.13023
- Hearts for commutative Noetherian rings: torsion pairs and derived equivalences, Documenta Mathematica, Volume 26 (2021), pp. 829-871 | DOI:10.25537/dm.2021v26.829-871 | Zbl:1471.13039
- Tempered D-modules and Borel-Moore homology vanishing, Inventiones Mathematicae, Volume 225 (2021) no. 2, pp. 453-528 | DOI:10.1007/s00222-021-01036-2 | Zbl:1485.14025
- Deligne–Lusztig duality on the stack of local systems, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2021 (2021) no. 778, p. 31 | DOI:10.1515/crelle-2021-0030
- Local Gorenstein duality for cochains on spaces, Journal of Pure and Applied Algebra, Volume 225 (2021) no. 2, p. 23 (Id/No 106495) | DOI:10.1016/j.jpaa.2020.106495 | Zbl:1451.55007
- The center of the categorified ring of differential operators, Journal of the European Mathematical Society (JEMS), Volume 23 (2021) no. 6, pp. 1999-2049 | DOI:10.4171/jems/1048 | Zbl:1506.14031
- Cohomological supports over derived complete intersections and local rings, Mathematische Zeitschrift, Volume 299 (2021) no. 3-4, pp. 2063-2101 | DOI:10.1007/s00209-021-02738-2 | Zbl:1476.13021
- Local duality for the singularity category of a finite dimensional Gorenstein algebra, Nagoya Mathematical Journal, Volume 244 (2021), pp. 1-24 | DOI:10.1017/nmj.2020.2 | Zbl:1493.16010
- Rank varieties and
-points for elementary supergroup schemes, Transactions of the American Mathematical Society. Series B, Volume 8 (2021), pp. 971-998 | DOI:10.1090/btran/74 | Zbl:1483.14090 - Hochschild cohomology of torus equivariant D-modules, IMRN. International Mathematics Research Notices, Volume 2020 (2020) no. 19, pp. 6391-6420 | DOI:10.1093/imrn/rny206 | Zbl:1483.14003
- Homological support of big objects in tensor-triangulated categories, Journal de l'École Polytechnique – Mathématiques, Volume 7 (2020), pp. 1069-1088 | DOI:10.5802/jep.135 | Zbl:1454.18005
- Support and rank varieties of totally acyclic complexes, Journal of Commutative Algebra, Volume 12 (2020) no. 2, pp. 293-308 | DOI:10.1216/jca.2020.12.293 | Zbl:1442.13040
- Support varieties – an axiomatic approach, Mathematische Zeitschrift, Volume 295 (2020) no. 1-2, pp. 395-426 | DOI:10.1007/s00209-019-02343-4 | Zbl:1505.18020
- Hall-type algebras for categorical Donaldson-Thomas theories on local surfaces, Selecta Mathematica. New Series, Volume 26 (2020) no. 4, p. 71 (Id/No 64) | DOI:10.1007/s00029-020-00592-4 | Zbl:1445.14076
- Flat ring epimorphisms and universal localizations of commutative rings, The Quarterly Journal of Mathematics, Volume 71 (2020) no. 4, p. 1489 | DOI:10.1093/qmath/haaa041
- The Cohen-Macaulay property in derived commutative algebra, Transactions of the American Mathematical Society, Volume 373 (2020) no. 9, pp. 6095-6138 | DOI:10.1090/tran/8099 | Zbl:1457.13023
- A physical origin for singular support conditions in geometric Langlands theory, Communications in Mathematical Physics, Volume 368 (2019) no. 3, pp. 985-1050 | DOI:10.1007/s00220-019-03438-z | Zbl:1434.14007
- Local duality for representations of finite group schemes, Compositio Mathematica, Volume 155 (2019) no. 2, pp. 424-453 | DOI:10.1112/s0010437x19007061 | Zbl:1509.16012
- Sheaves of categories with local actions of Hochschild cochains, Compositio Mathematica, Volume 155 (2019) no. 8, pp. 1521-1567 | DOI:10.1112/s0010437x19007413 | Zbl:1448.14015
- Localizing subcategories in the bootstrap category of filtered
-algebras, Journal of Noncommutative Geometry, Volume 13 (2019) no. 4, pp. 1209-1233 | DOI:10.4171/jncg/354 | Zbl:1435.19003 - Külshammer ideals of graded categories and Hochschild cohomology, Algebras and Representation Theory, Volume 21 (2018) no. 6, pp. 1251-1275 | DOI:10.1007/s10468-017-9746-4 | Zbl:1408.16006
- Cosupport computations for finitely generated modules over commutative noetherian rings, Journal of Algebra, Volume 511 (2018), pp. 249-269 | DOI:10.1016/j.jalgebra.2018.06.014 | Zbl:1439.13035
- Local duality for structured ring spectra, Journal of Pure and Applied Algebra, Volume 222 (2018) no. 2, pp. 433-463 | DOI:10.1016/j.jpaa.2017.04.012 | Zbl:1384.55008
- A local duality principle in derived categories of commutative Noetherian rings, Journal of Pure and Applied Algebra, Volume 222 (2018) no. 9, pp. 2580-2595 | DOI:10.1016/j.jpaa.2017.10.008 | Zbl:1407.13016
- The category of singularities as a crystal and global Springer fibers, Journal of the American Mathematical Society, Volume 31 (2018) no. 1, pp. 135-214 | DOI:10.1090/jams/882 | Zbl:1388.14042
- Stratification for module categories of finite group schemes, Journal of the American Mathematical Society, Volume 31 (2018) no. 1, pp. 265-302 | DOI:10.1090/jams/887 | Zbl:1486.16011
- The algebraic chromatic splitting conjecture for Noetherian ring spectra, Mathematische Zeitschrift, Volume 290 (2018) no. 3-4, pp. 1359-1375 | DOI:10.1007/s00209-018-2066-5 | Zbl:1476.55025
- Mini-workshop: Chromatic phenomena and duality in homotopy theory and representation theory. Abstracts from the mini-workshop held March 4–10, 2018, Oberwolfach Rep. 15, No. 1, 507-529, 2018 | DOI:10.4171/owr/2018/9 | Zbl:1409.00065
- Localization functors and cosupport in derived categories of commutative Noetherian rings, Pacific Journal of Mathematics, Volume 296 (2018) no. 2, pp. 405-435 | DOI:10.2140/pjm.2018.296.405 | Zbl:1411.13023
- Tensor triangular geometry for classical Lie superalgebras, Advances in Mathematics, Volume 314 (2017), pp. 228-277 | DOI:10.1016/j.aim.2017.04.022 | Zbl:1419.17011
- Colocalising subcategories of modules over finite group schemes, Annals of
-Theory, Volume 2 (2017) no. 3, pp. 387-408 | DOI:10.2140/akt.2017.2.387 | Zbl:1390.20009 - The characteristic morphism of an algebra, Applied Categorical Structures, Volume 25 (2017) no. 6, pp. 971-990 | DOI:10.1007/s10485-016-9437-z | Zbl:1392.16010
- Tests for injectivity of modules over commutative rings, Collectanea Mathematica, Volume 68 (2017) no. 2, pp. 243-250 | DOI:10.1007/s13348-016-0176-0 | Zbl:1372.13007
- A spectral incarnation of affine character sheaves, Compositio Mathematica, Volume 153 (2017) no. 9, pp. 1908-1944 | DOI:10.1112/s0010437x17007278 | Zbl:1439.20004
- Adically finite chain complexes, Journal of Algebra and its Applications, Volume 16 (2017) no. 12, p. 23 (Id/No 1750232) | DOI:10.1142/s0219498817502322 | Zbl:1394.13010
- Stratification and
-cosupport: finite groups, Mathematische Zeitschrift, Volume 287 (2017) no. 3-4, pp. 947-965 | DOI:10.1007/s00209-017-1853-8 | Zbl:1483.20088 - Extended local cohomology and local homology, Algebras and Representation Theory, Volume 19 (2016) no. 5, pp. 1217-1238 | DOI:10.1007/s10468-016-9616-5 | Zbl:1360.13025
- Depth for triangulated categories, Bulletin of the Korean Mathematical Society, Volume 53 (2016) no. 2, pp. 551-559 | DOI:10.4134/bkms.2016.53.2.551 | Zbl:1346.18017
- Realizations of pairs and Oka families in tensor triangulated categories, European Journal of Mathematics, Volume 2 (2016) no. 3, pp. 760-797 | DOI:10.1007/s40879-016-0108-2 | Zbl:1361.13002
- A thick subcategory theorem for modules over certain ring spectra, Geometry Topology, Volume 19 (2015) no. 4, pp. 2359-2392 | DOI:10.2140/gt.2015.19.2359 | Zbl:1405.55009
- A local-global principle for small triangulated categories, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 158 (2015) no. 3, pp. 451-476 | DOI:10.1017/s0305004115000067 | Zbl:1371.18008
- Singular support of coherent sheaves and the geometric Langlands conjecture, Selecta Mathematica. New Series, Volume 21 (2015) no. 1, pp. 1-199 | DOI:10.1007/s00029-014-0167-5 | Zbl:1423.14085
- Matrix factorizations in higher codimension, Transactions of the American Mathematical Society, Volume 367 (2015) no. 5, pp. 3323-3370 | DOI:10.1090/s0002-9947-2015-06323-5 | Zbl:1394.13016
- On the string topology category of compact Lie groups, Advances in Mathematics, Volume 261 (2014), pp. 122-153 | DOI:10.1016/j.aim.2014.05.002 | Zbl:1309.55006
- Examples of support varieties for Hopf algebras with noncommutative tensor products., Archiv der Mathematik, Volume 102 (2014) no. 6, pp. 513-520 | DOI:10.1007/s00013-014-0659-8 | Zbl:1310.16025
- Spectra of tensor triangulated categories over category algebras, Archiv der Mathematik, Volume 103 (2014) no. 3, pp. 235-253 | DOI:10.1007/s00013-014-0684-7 | Zbl:1309.18014
- On growth in minimal totally acyclic complexes, Journal of Commutative Algebra, Volume 6 (2014) no. 1, pp. 17-31 | DOI:10.1216/jca-2014-6-1-17 | Zbl:1304.13030
- Stratifying the derived category of cochains on
for a compact Lie group, Journal of Pure and Applied Algebra, Volume 218 (2014) no. 4, pp. 642-650 | DOI:10.1016/j.jpaa.2013.08.004 | Zbl:1291.18014 - On the derived category of a graded commutative noetherian ring, Journal of Algebra, Volume 373 (2013), pp. 356-376 | DOI:10.1016/j.jalgebra.2012.09.038 | Zbl:1272.13002
- Thick subcategories over Gorenstein local rings that are locally hypersurfaces on the punctured spectra, Journal of the Mathematical Society of Japan, Volume 65 (2013) no. 2, pp. 357-374 | DOI:10.2969/jmsj/06520357 | Zbl:1314.13029
- The Bousfield lattice of a triangulated category and stratification, Mathematische Zeitschrift, Volume 273 (2013) no. 3-4, pp. 1215-1241 | DOI:10.1007/s00209-012-1051-7 | Zbl:1328.18017
- Stratifying derived categories of cochains on certain spaces, Mathematische Zeitschrift, Volume 272 (2012) no. 3-4, pp. 839-868 | DOI:10.1007/s00209-011-0960-1 | Zbl:1271.55010
- The Hochschild cohomology ring of the singular cochain algebra of a space., Annales de l'Institut Fourier, Volume 61 (2011) no. 5, pp. 1779-1805 | DOI:10.5802/aif.2658 | Zbl:1279.16009
- Stratifying modular representations of finite groups., Annals of Mathematics. Second Series, Volume 174 (2011) no. 3, pp. 1643-1684 | DOI:10.4007/annals.2011.174.3.6 | Zbl:1261.20057
- Localising subcategories for cochains on the classifying space of a finite group, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 349 (2011) no. 17-18, pp. 953-956 | DOI:10.1016/j.crma.2011.08.019 | Zbl:1237.18009
- On the local cohomology and support for triangulated categories, Kyoto Journal of Mathematics, Volume 51 (2011) no. 4, pp. 811-829 | DOI:10.1215/21562261-1424866 | Zbl:1254.18009
- Module categories for finite group algebras., Representations of algebras and related topics. Proceedings of the 14th international conference on representations of algebras and workshop (ICRA XIV), Tokyo, Japan, August 6–15, 2010., Zürich: European Mathematical Society (EMS), 2011, pp. 55-83 | Zbl:1301.16010
- The telescope conjecture for hereditary rings via Ext-orthogonal pairs., Advances in Mathematics, Volume 225 (2010) no. 5, pp. 2341-2364 | DOI:10.1016/j.aim.2010.04.027 | Zbl:1242.16007
- Spectra, spectra, spectra – tensor triangular spectra versus Zariski spectra of endomorphism rings, Algebraic Geometric Topology, Volume 10 (2010) no. 3, pp. 1521-1563 | DOI:10.2140/agt.2010.10.1521 | Zbl:1204.18005
- Dimensions of triangulated categories via Koszul objects, Mathematische Zeitschrift, Volume 265 (2010) no. 4, pp. 849-864 | DOI:10.1007/s00209-009-0545-4 | Zbl:1263.18006
- The
-core and -cover of a group., Journal of Algebra, Volume 321 (2009) no. 2, pp. 631-666 | DOI:10.1016/j.jalgebra.2008.09.022 | Zbl:1213.20049 - On the support of local cohomology, Journal of Algebra, Volume 322 (2009) no. 9, pp. 3194-3211 | DOI:10.1016/j.jalgebra.2008.02.021 | Zbl:1186.13016
- Thick subcategories of modules over commutative noetherian rings (with an appendix by Srikanth Iyengar), Mathematische Annalen, Volume 340 (2008) no. 4, pp. 733-747 | DOI:10.1007/s00208-007-0166-3 | Zbl:1143.13012
- The telescope conjecture for hereditary rings via Ext-orthogonal pairs, arXiv (2008) | DOI:10.48550/arxiv.0810.1401 | arXiv:0810.1401
- Thick subcategories of modules over commutative rings, arXiv (2007) | DOI:10.48550/arxiv.math/0703158 | arXiv:math/0703158
- Modules with prescribed cohomological support, arXiv (2007) | DOI:10.48550/arxiv.math/0702654 | arXiv:math/0702654
Cité par 91 documents. Sources : Crossref, NASA ADS, zbMATH