Sur la théorie des corps de classes pour les variétés sur les corps p -adiques
Thèses d'Orsay, no. 531 (1998) , 72 p. 
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     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://www.numdam.org/item/BJHTUP11_1998__0531__P0_0/}
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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] A. Beauville. - Surfaces algébriques complexes, 3e éd., Astérisque 54, 1978. | MR | Zbl | Numdam

[2] A. A. Beilinson. - Lettre à C. Soulé, 1982.

[3] S. Bloch. - Algebraic K-theory and class field theory for arithmetic surfaces, Ann. of Math. 114 (1981), 229-265. | MR | Zbl | DOI

[4] S. Bloch. - Lectures on Algebraic Cycles, Duke University, 1980. | MR | Zbl

[5] S. Bloch and A. Ogus. - Gersten's conjecture and the homology of schemes, Ann. Sci. ENS 4e sér. 7 (1974), 181-202. | MR | Zbl | Numdam

[6] S. Bosch, W. Lütkebohmert, M. Raynaud. - Néron Models, Springer, 1990. | MR | Zbl | DOI

[7] G. Bredon. - Sheaf Theory, 2nd ed, Springer GTM 170, 1997. | MR | Zbl

[8] J.-L. Colliot-Thélène. - 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] J.-L. Colliot-Thélène, R. Hoobler and B. Kahn. - The Bloch-Ogus-Gabber theorem, Fields Institute Communications 16 (1997), 31-94. | MR | Zbl

[10] J.-L. Colliot-Thélène and W. Raskind. - K2-cohomology and the second Chow group, Math. Ann. 270 (1985), 165-199. | MR | Zbl | DOI

[11] J.-L. Colliot-Thélène and W. Raskind. - 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

[12] J.-L. Colliot-Thélène, J.-J. Sansuc et C. Soulé. - Torsion dans le groupe de Chow de codimension deux, Duke Math. J. 50 (1983), 763-801. | MR | Zbl

[13] P. Deligne. - La conjecture de Weil II, Publ. Math. IHES 52 (1980), 137-252. | MR | Zbl | Numdam

[14] J. Gamst and K. Hoechsmann. - Products in Sheaf-Cohomology, Tohoku Math. J. 22 (1970), 143-162. | MR | Zbl | DOI

[15] U. Jannsen. - On the l -adic cohomology of varieties over number fields and its Galois cohomology, in Galois Groups over ℚ (Y. Ihara, K. Ribet, J-P. Serre, eds.) Springer, 1989, 315-360 | MR | Zbl | DOI

[16] K. Kato. - A Hasse principle for two-dimensional global fields, J. reine angew. Math. 366 (1986), 142-181. | MR | Zbl

[17] S. Lang. - Unramified class field theory over function fields in several variables, Ann. of Math. 64 (1956), 555-563. | MR | Zbl | DOI

[18] A. Merkur'Ev and A. Suslin. - 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

[19] A. Merkur'Ev and A. Suslin. - 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

[20] J. S. Milne. - Étale cohomology, Princeton Univ. Press, 1980. | MR | Zbl

[21] W. Raskind. - Higher class field theory of arithmetic schemes, Proc. Symp. Pure Math. 58/1 (1995), 85-187. | MR | Zbl | DOI

[22] S. Saito. - Class field theory of curves over local fields, J. Number Theory 21 (1985), 44-80. | MR | Zbl | DOI

[23] S. Saito. - Unramified class field theory of arithmetic schemes, Ann. of Math. 121 (1985), 251-281. | MR | Zbl | DOI

[24] S. Saito. - 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] S. Saito. - Cycle map on torsion algebraic cycles of codimension two, Invent. Math. 106 (1991), 443-460. | MR | Zbl

[26] S. Saito and P. Salberger, Class field theory for surfaces over local fields , TEX-script non publié, 1993.

[27] K. Sato. - Finiteness of a certain motivic cohomology of varieties : application to regulator maps, prépublication, 1998.

[28] T. Sato. - Torsion of SK1 of curves over local fields, tapuscript non publié.

[29] J.-P. Serre. - Cohomologie galoisienne (5e éd.), Springer LNM 5, 1994. | MR | Zbl

[30] C. Soulé. - The rank of étale cohomology of varieties over p-adic or number fields, Compositio Math. 53 (1984), 113-131. | MR | Zbl | Numdam

[31] A. Suslin. - 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] A. Suslin. - Torsion in K2 of fields, K-Theory 1 (1987), 5-29. | MR | Zbl | DOI

[33] A. Suslin and V. Voevodsky. - Bloch-Kato conjecture and motivic cohomology with finite coefficients, prépublication, 1995. | Zbl

[34] T. Szamuely. - Sur la loi de réciprocité de Kato pour les anneaux locaux de dimension 2, L'Enseignement Mathématique 43 (1997), 77-91. | MR | Zbl

[35] T. Szamuely. - Sur l'application de réciprocité pour une surface fibrée en coniques définie sur un corps local, prépublication. | Zbl

[36] V. Voevodsky. - Triangulated categories of motives over a field, prépublication, 1995. | Zbl

[37] V. Voevodsky. - Cohomological theory of presheaves with transfers, prépublication, 1995. | Zbl

[38] V. Voevodsky. - The Milnor Conjecture, prépublication, 1996.

[39] C. Weibel. - An Introduction to Homological Algebra, Cambridge University Press, 1995. | Zbl | MR

[SGA1] A. Grothendieck. - Revêtements étales et groupe fondamental, Springer LNM 224, 1971.

[1] R. Alperin, R.K. Dennis. - K2 o f quaternion algebras, J. Algebra 56 (1979), 262-274. | MR | Zbl | DOI

[2] H. Bass, J. Tate. - The Milnor ring of a global field, in Algebraic K-Theory II, Springer LNM 342, 1973. | MR | Zbl

[3] J-L. Colliot-Thélène, A. N. Skorobogatov. - Groupe de Chow des zéro-cycles sur les fibrés en quadriques, K-Theory 7 (1993), 477-500. | MR | Zbl | DOI

[4] R Draxl. - Skew Fields, LMS Lecture Notes 81, Cambridge University Press, 1983. | MR | Zbl

[5] H. Gillet. - Riemann-Roch theorems for higher algebraic K-theory, Adv. in Math. 40 (1981), 203-289. | MR | Zbl

[6] B. Iversen. - Cohomology of Sheaves, Springer, 1986. | MR | Zbl | DOI

[7] Yu. I. Manin. - 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] Yu. I. Manin. - Cubic Forms, North-Holland, 1974. | Zbl

[9] A.S. Merkurjev. - K-theory of simple algebras, Proc. Symp. Pure Math. 58/1 (1995), 65-83. | MR | Zbl | DOI

[10] R. Parimala, V. Suresh. - Zero-cycles on quadric fibrations : Finiteness theorems and the cycle map, Inv. Math. 122 (1995), 83-119. | MR | Zbl

[11] W. Raskind. - Higher class field theory of arithmetic schemes, Proc. Symp. Pure Math. 58/1 (1995), 85-187. | MR | Zbl | DOI

[12] U. Rehmann, U. Stuhler. - On K2 of finite dimensional division algebras over arithmetical fields, Inv. Math. 50 (1978), 75-90. | MR | Zbl

[13] S. Saito. - Class field theory of curves over local fields, J. Number Theory 21 (1985), 44-80. | MR | Zbl | DOI

[14] S. Saito. - Unramified class field theory of arithmetic schemes, Ann. of Math. 121 (1985), 251-281. | MR | Zbl

[15] A. Weil. - Basic Number Theory, 2nd ed, Springer, 1973. | Zbl

[1] M. Artin. - Algebraic approximation of structures over complete local rings, Pub. Math. IHES 36 (1969), 23-58. | MR | Zbl | Numdam

[2] M. Artin. - Grothendieck Topologies, Harvard University, 1961. | Zbl

[3] H. Bass and J. Tate. - The Milnor Ring of a Global Field, in : H. Bass (ed.) Algebraic K-theory II, Springer LNM 342, 1973. | MR | Zbl

[4] S. Bloch. - Lectures on Algebraic Cycles, Duke University, 1980. | MR | Zbl

[5] E. Frossard. - Thèse, Université de Paris-XI, Orsay, 1995.

[6] K. Kato. - A generalization of local class field theory by using K-groups II, J. Fac. Sci. Univ. Tokyo, 27 (1980), 603-683. | MR | Zbl

[7] K. Kato. - 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] K. Kato. - A Hasse principle for two-dimensional local fields, J. reine angew. Math. 366 (1986), 142-183. | MR | Zbl

[9] K. Kato and S. Saito. - 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

[10] S. Lang. - Algebra (3rd ed.), Addison-Wesley, 1993. | Zbl

[11] J. S. Milne. - Étale Cohomology, Princeton University Press, 1980. | MR | Zbl

[12] M. Nagata. - Local Rings, Wiley-Interscience, New York, 1952. | MR | Zbl

[13] B. Perrin-Riou. - Systèmes d'Euler et représentations p-adiques, prépublication Orsay 96-04.

[14] S. Saito. - Class field theory for curves over local fields, J. Number Theory 21 (1985), 44-80. | MR | Zbl | DOI

[15] J.-P. Serre. - Cohomologie Galoisienne (5e éd.), Springer LNM 5, 1994. | MR | Zbl

[16] J.-P. Serre. - Corps locaux, Hermann, Paris, 1968. | MR | Zbl

[17] J.-P. Serre. - 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] J. Tate. - 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] J. Tate. - Relations between K2 and Galois cohomology, Invent. Math. 36 (1976), 257-274. | MR | Zbl