@phdthesis{BJHTUP11_1998__0531__P0_0, author = {Szamuely, Tamas}, title = {Sur la th\'eorie des corps de classes pour les vari\'et\'es sur les corps $p$-adiques}, series = {Th\`eses d'Orsay}, publisher = {Universit\'e de Paris-Sud Centre d'Orsay}, number = {531}, year = {1998}, language = {fr}, url = {http://archive.numdam.org/item/BJHTUP11_1998__0531__P0_0/} }
TY - BOOK AU - Szamuely, Tamas TI - Sur la théorie des corps de classes pour les variétés sur les corps $p$-adiques T3 - Thèses d'Orsay PY - 1998 IS - 531 PB - Université de Paris-Sud Centre d'Orsay UR - http://archive.numdam.org/item/BJHTUP11_1998__0531__P0_0/ LA - fr ID - BJHTUP11_1998__0531__P0_0 ER -
Szamuely, Tamas. Sur la théorie des corps de classes pour les variétés sur les corps $p$-adiques. Thèses d'Orsay, no. 531 (1998), 72 p. http://numdam.org/item/BJHTUP11_1998__0531__P0_0/
[1] Surfaces algébriques complexes, 3e éd., Astérisque 54, 1978. | MR | Zbl | Numdam
. -[2] Lettre à C. Soulé, 1982.
. -[3] Algebraic K-theory and class field theory for arithmetic surfaces, Ann. of Math. 114 (1981), 229-265. | MR | Zbl | DOI
. -[4] Lectures on Algebraic Cycles, Duke University, 1980. | MR | Zbl
. -[5] Gersten's conjecture and the homology of schemes, Ann. Sci. ENS 4e sér. 7 (1974), 181-202. | MR | Zbl | Numdam
and . -[6] Néron Models, Springer, 1990. | MR | Zbl | DOI
, , . -[7] Sheaf Theory, 2nd ed, Springer GTM 170, 1997. | MR | Zbl
. -[8] On the reciprocity sequence in the higher class field theory of function fields, in K-Theory and Algebraic Topology (P. G. Goerss, J. F. Jardine, eds.) Kluwer, 1993. | MR | Zbl | DOI
. -[9] The Bloch-Ogus-Gabber theorem, Fields Institute Communications 16 (1997), 31-94. | MR | Zbl
, and . -[10] K2-cohomology and the second Chow group, Math. Ann. 270 (1985), 165-199. | MR | Zbl | DOI
and . -[11] Groupe de Chow de codimension deux des variétés définies sur un corps de nombres : un théorème de finitude sur la torsion, Invent. Math. 105 (1991), 221-245. | MR | Zbl
and . -[12] Torsion dans le groupe de Chow de codimension deux, Duke Math. J. 50 (1983), 763-801. | MR | Zbl
, et . -[13] La conjecture de Weil II, Publ. Math. IHES 52 (1980), 137-252. | MR | Zbl | Numdam
. -[14] Products in Sheaf-Cohomology, Tohoku Math. J. 22 (1970), 143-162. | MR | Zbl | DOI
and . -[15] On the -adic cohomology of varieties over number fields and its Galois cohomology, in Galois Groups over (Y. Ihara, K. Ribet, J-P. Serre, eds.) Springer, 1989, 315-360 | MR | Zbl | DOI
. -[16] A Hasse principle for two-dimensional global fields, J. reine angew. Math. 366 (1986), 142-181. | MR | Zbl
. -[17] Unramified class field theory over function fields in several variables, Ann. of Math. 64 (1956), 555-563. | MR | Zbl | DOI
. -[18] K-cohomology of Severi-Brauer varieties and the norm residue homomorphism. Version russe : Izv. Akad. Nauk SSSR 46 (1982) No. 5. Version anglaise : Math. USSR Izvestiya 21 (1983), 307-340. | MR | Zbl
and . -[19] The group K3 for a field. Version russe : Izv. Akad. Nauk SSSR 54 (1990) No. 3. Version anglaise : Math. USSR Izvestiya 36 (1991), 541-565. | Zbl | MR
and . -[20] Étale cohomology, Princeton Univ. Press, 1980. | MR | Zbl
. -[21] Higher class field theory of arithmetic schemes, Proc. Symp. Pure Math. 58/1 (1995), 85-187. | MR | Zbl | DOI
. -[22] Class field theory of curves over local fields, J. Number Theory 21 (1985), 44-80. | MR | Zbl | DOI
. -[23] Unramified class field theory of arithmetic schemes, Ann. of Math. 121 (1985), 251-281. | MR | Zbl | DOI
. -[24] A global duality theorem for varieties over number fields, in Algebraic K- Theory : Connections with Geometry and Topology (J. F. Jardine and V. P. Snaith, eds.), Kluwer, 1989. | MR | Zbl
. -[25] Cycle map on torsion algebraic cycles of codimension two, Invent. Math. 106 (1991), 443-460. | MR | Zbl
. -[26] Class field theory for surfaces over local fields , TEX-script non publié, 1993.
and ,[27] Finiteness of a certain motivic cohomology of varieties : application to regulator maps, prépublication, 1998.
. -[28] Torsion of SK1 of curves over local fields, tapuscript non publié.
. -[29] Cohomologie galoisienne (5e éd.), Springer LNM 5, 1994. | MR | Zbl
. -[30] The rank of étale cohomology of varieties over p-adic or number fields, Compositio Math. 53 (1984), 113-131. | MR | Zbl | Numdam
. -[31] Algebraic K-theory and the norm residue homomorphism. Version russe : Itogi Nauki i Tehniki, Sovrem. Prob. Mat. Nov. Dost. 25 (1984), 115-207. Version anglaise : J. Soviet Math. 30 (1985), 2556-2611. | Zbl | MR
. -[32] Torsion in K2 of fields, K-Theory 1 (1987), 5-29. | MR | Zbl | DOI
. -[33] Bloch-Kato conjecture and motivic cohomology with finite coefficients, prépublication, 1995. | Zbl
and . -[34] Sur la loi de réciprocité de Kato pour les anneaux locaux de dimension 2, L'Enseignement Mathématique 43 (1997), 77-91. | MR | Zbl
. -[35] Sur l'application de réciprocité pour une surface fibrée en coniques définie sur un corps local, prépublication. | Zbl
. -[36] Triangulated categories of motives over a field, prépublication, 1995. | Zbl
. -[37] Cohomological theory of presheaves with transfers, prépublication, 1995. | Zbl
. -[38] The Milnor Conjecture, prépublication, 1996.
. -[39] An Introduction to Homological Algebra, Cambridge University Press, 1995. | Zbl | MR
. -[SGA1] Revêtements étales et groupe fondamental, Springer LNM 224, 1971.
. -[1] K2 o f quaternion algebras, J. Algebra 56 (1979), 262-274. | MR | Zbl | DOI
, . -[2] The Milnor ring of a global field, in Algebraic K-Theory II, Springer LNM 342, 1973. | MR | Zbl
, . -[3] Groupe de Chow des zéro-cycles sur les fibrés en quadriques, K-Theory 7 (1993), 477-500. | MR | Zbl | DOI
, . -[4] Skew Fields, LMS Lecture Notes 81, Cambridge University Press, 1983. | MR | Zbl
-[5] Riemann-Roch theorems for higher algebraic K-theory, Adv. in Math. 40 (1981), 203-289. | MR | Zbl
. -[6] Cohomology of Sheaves, Springer, 1986. | MR | Zbl | DOI
. -[7] Surfaces rationnelles sur les corps parfaits I. (en russe) Publ. Math. IHES 30 (1966), 55-113. (Trad. anglaise : Amer. Math. Soc. Transl. 84 (1969), 137-186.) | Zbl
. -[8] Cubic Forms, North-Holland, 1974. | Zbl
. -[9] K-theory of simple algebras, Proc. Symp. Pure Math. 58/1 (1995), 65-83. | MR | Zbl | DOI
. -[10] Zero-cycles on quadric fibrations : Finiteness theorems and the cycle map, Inv. Math. 122 (1995), 83-119. | MR | Zbl
, . -[11] Higher class field theory of arithmetic schemes, Proc. Symp. Pure Math. 58/1 (1995), 85-187. | MR | Zbl | DOI
. -[12] On K2 of finite dimensional division algebras over arithmetical fields, Inv. Math. 50 (1978), 75-90. | MR | Zbl
, . -[13] Class field theory of curves over local fields, J. Number Theory 21 (1985), 44-80. | MR | Zbl | DOI
. -[14] Unramified class field theory of arithmetic schemes, Ann. of Math. 121 (1985), 251-281. | MR | Zbl
. -[15] Basic Number Theory, 2nd ed, Springer, 1973. | Zbl
. -[1] Algebraic approximation of structures over complete local rings, Pub. Math. IHES 36 (1969), 23-58. | MR | Zbl | Numdam
. -[2] Grothendieck Topologies, Harvard University, 1961. | Zbl
. -[3] The Milnor Ring of a Global Field, in : H. Bass (ed.) Algebraic K-theory II, Springer LNM 342, 1973. | MR | Zbl
and . -[4] Lectures on Algebraic Cycles, Duke University, 1980. | MR | Zbl
. -[5] Thèse, Université de Paris-XI, Orsay, 1995.
. -[6] A generalization of local class field theory by using K-groups II, J. Fac. Sci. Univ. Tokyo, 27 (1980), 603-683. | MR | Zbl
. -[7] Milnor K-theory and the Chow group of zero-cycles, in : S. Bloch et al. (eds.) Applications of Algebraic K-Theory to Algebraic Geometry and Number Theory, Contemp. Math. 55 (1986), 241-263. | MR | Zbl | DOI
. -[8] A Hasse principle for two-dimensional local fields, J. reine angew. Math. 366 (1986), 142-183. | MR | Zbl
. -[9] Global class field theory of arithmetic schemes, in : S. Bloch et al. (eds.) Applications of Algebraic K-Theory to Algebraic Geometry and Number Theory, Contemp. Math. 55 (1986), 255-331. | MR | Zbl | DOI
and . -[10] Algebra (3rd ed.), Addison-Wesley, 1993. | Zbl
. -[11] Étale Cohomology, Princeton University Press, 1980. | MR | Zbl
. -[12] Local Rings, Wiley-Interscience, New York, 1952. | MR | Zbl
. -[13] Systèmes d'Euler et représentations p-adiques, prépublication Orsay 96-04.
. -[14] Class field theory for curves over local fields, J. Number Theory 21 (1985), 44-80. | MR | Zbl | DOI
. -[15] Cohomologie Galoisienne (5e éd.), Springer LNM 5, 1994. | MR | Zbl
. -[16] Corps locaux, Hermann, Paris, 1968. | MR | Zbl
. -[17] Local class field theory, in : J. W. S. Cassels and A. Fröhlich (eds.) Algebraic Number Theory, Academic Press, London-New York, 1967, 129-162
. -[18] Global class field theory, in : J. W. S. Cassels and A. Fröhlich (eds.) Algebraic Number Theory, Academic Press, London-New York, 1967, 163-203 | MR | Zbl
. -[19] Relations between K2 and Galois cohomology, Invent. Math. 36 (1976), 257-274. | MR | Zbl
. -