Obstructions for deformations of complexes
Annales de l'Institut Fourier, Volume 63 (2013) no. 2, p. 613-654
We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes of modules for a profinite group G over a complete local Noetherian ring A of positive residue characteristic.
Nous développons deux approches de la théorie de l’obstruction des déformations de classes d’isomorphisme dans la catégorie dérivée des complexes de A[[G]]-modules lorsque G est un groupe profini et A un anneau local, noethérien complet, de caractéristique positive résiduelle.
DOI : https://doi.org/10.5802/aif.2771
Classification:  11F80,  20E18,  18E30,  18G40
Keywords: Versal and universal deformations, derived categories, obstructions, spectral sequences 
@article{AIF_2013__63_2_613_0,
     author = {Bleher, Frauke M. and Chinburg, Ted},
     title = {Obstructions for deformations of complexes},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {2},
     year = {2013},
     pages = {613-654},
     doi = {10.5802/aif.2771},
     mrnumber = {3112843},
     zbl = {06193042},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2013__63_2_613_0}
}

Bleher, Frauke M.; Chinburg, Ted. Obstructions for deformations of complexes. Annales de l'Institut Fourier, Volume 63 (2013) no. 2, pp. 613-654. doi : 10.5802/aif.2771. http://www.numdam.org/item/AIF_2013__63_2_613_0/

[1] Bleher, Frauke M.; Chinburg, Ted Deformations and derived categories, Ann. Institut Fourier (Grenoble), Tome 55 (2005), pp. 2285-2359 | Article | Numdam | MR 2207385 | Zbl 1138.11020

[2] Bleher, Frauke M.; Chinburg, Ted Finiteness Theorems for Deformations of Complexes., Ann. Institut Fourier (Grenoble), Tome 63 (2013), pp. 573-612 | Article

[3] Brumer, Armand Pseudocompact algebras, profinite groups and class formations, J. Algebra, Tome 4 (1966), pp. 442-470 | Article | MR 202790 | Zbl 0146.04702

[4] Gabriel, Pierre Des catégories abéliennes, Bull. Soc. Math. France, Tome 90 (1962), pp. 323-448 | Numdam | MR 232821 | Zbl 0201.35602

[5] Gabriel, Pierre Étude infinitésimale des schémas en groupes, A. Grothendieck, SGA 3 (with M. Demazure), Schémas en groupes I, II, III, Springer-Verlag, Heidelberg (Lecture Notes in Math. 151) (1970), pp. 476- 562 | Zbl 0209.24201

[6] Grothendieck, A.; Dieudonné, J. Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I, II, Inst. Hautes Études Sci. Publ. Math. (1961 and 1963) no. 11 and 17, pp. 91 and 167 | Numdam | MR 217085 | Zbl 0122.16102

[7] Illusie, Luc Complexe cotangent et déformations. I, II, Springer-Verlag, Berlin, Lecture Notes in Mathematics, Vol. 239 and 283 (1971 and 1972) | MR 491680 | Zbl 0224.13014

[8] Mazur, B. Deforming Galois representations, Galois groups over Q (Berkeley, CA, 1987), Springer Verlag, Berlin-Heidelberg-New York (Math. Sci. Res. Inst. Publ.) Tome 16 (1989), pp. 385-437 | MR 1012172 | Zbl 0714.11076

[9] Mazur, B. Deformation theory of Galois representations, Modular Forms and Fermat’s Last Theorem (Boston, MA, 1995), Springer Verlag, Berlin-Heidelberg-New York (1997), pp. 243-311 | MR 1638481

[10] Schlessinger, Michael Functors of Artin rings, Trans. Amer. Math. Soc., Tome 130 (1968), pp. 208-222 | Article | MR 217093 | Zbl 0167.49503

[11] Verdier, J.-L. Catégories derivées, P. Deligne, SGA 4.5, Cohomologie étale, Springer Verlag, Heidelberg (Lecture Notes in Math. 569) (1970), pp. 262-311