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K-théorie des anneaux d’entiers de corps de nombres et cohomologie etale. (French) Zbl 0437.12008

MSC:
11R70 \(K\)-theory of global fields
11R80 Totally real fields
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
14F20 Étale and other Grothendieck topologies and (co)homologies
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
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References:
[1] Artin, M.: Grothendieck Topologies. Springer 1962 · Zbl 0208.48701
[2] Artin, M., Verdier, J.L.: Seminar on Etale Cohomology of number fields. AMS Summer Institute on Algebraic geometry 1964
[3] Bayer, P., Neukirch, J.: On values of zeta functions and ?-adic Euler characteristics. Inventiones math.50, 35-64 (1978) · Zbl 0409.12018 · doi:10.1007/BF01406467
[4] Bass, H.: AlgebraicK-theory. New York: Benjamin 1968 · Zbl 0174.30302
[5] Bass, H., Tate, J.: The Milnor ring of a global field. ?AlgebraicK-theory II?. Lecture Notes in Mathematics no. 342. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0299.12013
[6] Bloch, S.: Higher regulators, AlgebraicK-theory, and zeta functions of elliptic curves. Preprint
[7] Bloch, S.: AlgebraicK-theory and crystalline cohomology, I.H.E.S., no 47, 187-268 (1978) · Zbl 0388.14010
[8] Bloch, S.: Some formulas pertaining to theK-theory of commutative groupschemes. Preprint, 1977
[9] Bloch, S., Ogus, A.: Gersten’s Conjecture and the homology of schemes. Ann. Scient. Ec. Norm. Sup.,7, fasc. 2 (1974) · Zbl 0307.14008
[10] Borel, A.: Stable real cohomology of arithmetic groups. Ann. Scient. Ec. Norm. Sup., 4è série,7, 235-272 (1974) · Zbl 0316.57026
[11] Browder, W.: AlgebraicK-theory with coefficientsZ/p, dans ?Geometry applications of Homotopy Theory I?. Lecture notes in Mathematics no. 657. Berlin-Heidelberg-New York: Springer 1978
[12] Cartan, E., Eilenberg, S.: Homological Algebra, Princeton University Press, 1956
[13] Cassels, J.W., Fröhlich, A.: Algebraic Number Theory. New York-London: Academic Press, 1967 · Zbl 0153.07403
[14] Charney, R.: Homology Stability forGL n of a Dedekind domain, à paraître
[15] Coates, J., Lichtenbaum, S.: On ?-adic zêta functions. Annals of Maths.,98, 498-550 (1973) · Zbl 0279.12005 · doi:10.2307/1970916
[16] Deligne, P., Ribet, K.: Values of abelianL-functions at negative integers, à paraître aux Inventiones math. · Zbl 0434.12009
[17] Farrell, F.T., Hsiang, W.C.: On the rational homotopy groups of the diffeomorphisms groups of discs, spheres and aspherical manifolds. · Zbl 0393.55018
[18] Ferrero, B., Washington, L.C.: The Iwasawa invariant? p for abelian number fields. A paraître aux Annals of Maths. · Zbl 0443.12001
[19] Gillet, H.: The applications of AlgebraicK-theory to intersection theory. Thèse, preprint
[20] Grayson, D.: Higher AlgebraicK-theory II. Lecture notes in Mathematics no 551. Berlin-Heidelberg-New York: Springer 1976
[21] Grothendieck, A.: Classes de Chern et représentations linéaires des groupes discrets. Dans “10 exposés sur la cohomologie des schémas”. Masson: North-Holland 1968
[22] Grothendieck, A.: Eléments de Géométrie Algébrique, Chapitre 0, §13, Publications I.H.E.S. no 11, 1961
[23] Harris, B., Segal, G.:K i of rings of algebraic integers. Ann. of Maths.101, 20-33 (1975) · Zbl 0331.18015 · doi:10.2307/1970984
[24] Hiller, H.: ?-rings and algebraicK-theory. Preprint
[25] Illusie, L.: Lettre à Gersten, 24/2/1974
[26] Karoubi, M.: A paraître
[27] Kato, K.: A generalization of local class field theory by usingK-groups, I et II. Proc. Japan Acad.53, 140-143 (1977)54, 250-255 (1979) · Zbl 0379.32023 · doi:10.3792/pja/1195517920
[28] Kratzer, C.: Opérations d’Adams enK-théorie algébrique, Note aux C.R. Acad. Sc. Paris,287, Série A, 297 (1978) et article en préparation
[29] Lee, R., Szczarba, R.H.: The groupK 3(?) is cyclic of order 48, Ann. of Math.,104, 31-60 (1976) · Zbl 0341.18008 · doi:10.2307/1971055
[30] Lee, R., Szczarba, R.H.: On the torsion inK 4(?) andK 5(?). Duke Journal, 1978
[31] Lichtenbaum, S.: On the values of zéta andL-functions, I. Ann. of Maths.,96, 338-360 (1972) · Zbl 0251.12002 · doi:10.2307/1970792
[32] Lichtenbaum, S.: Values of zeta functions, étale cohomology, and algebraicK-theory. Dans ?Alg.K-theory II?. Lecture notes in Mathematics no 342. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0284.12005
[33] Loday, J.L.:K-théorie et représentations de groupes. Ann. Scient. Ec. Norm. Sup. 4ème série,9, 309-377 (1976)
[34] Maazen, H.: Stabilité de l’homologie deGL n . C.R. Acad. Sc. Paris,288, 707-708 (1979) · Zbl 0411.20028
[35] Milnor, J.: Introduction to AlgebraicK-theory. Annals of Maths. Studies no 72. Princeton
[36] Milnor, J., Stasheff, J.D.: Characteristic classes; Appendice, Annals of Maths. Studies, no67, 1974 · Zbl 0298.57008
[37] Parshin, A.I.: Corps de classes etK-théorie algébrique, Ouspekhi Math. N.T. 30,1, 253-254 (1975) (en russe), et “Class Field Theory for Arthmetical schemes”, preprint
[38] Quillen, D.: AlgebraicK-theory I. Lecture Notes no 341
[39] Quillen, D.: On the cohomology andK-theory of the general linear groups over a finite field. Annals of Maths.,96, 552-586 (1972) · Zbl 0249.18022 · doi:10.2307/1970825
[40] Quillen, D.: Lettre à Milnor sur \(\operatorname{Im} (\pi _i O\mathop \to \limits^J \pi _i^s \to K_i \mathbb{Z})\) . Lecture Notes in Mathematics no 551. Berlin-Heidelberg-New York: Springer 1976
[41] Quillen, D.: Finite generation of the groupsK i of rings of algebraic integers. Lecture Notes in Mathematics no 341, pp. 179-210. Berlin-Heidelberg-New York: Springer 1973
[42] Quillen, D.: Cours à M.I.T., 1974-75
[43] Raynaud, M.: Caractéristique d’Euler Poincaré d’un faisceau et cohomologie des variétés abéliennes, dans “dix exposés sur la cohomologie des schémas”, north Holland: Masson 1968
[44] Séminaire de Géométrie Algébrique IV: Exposé VIII, A. Grothendieck, Lecture notes in Mathematics no 270. Berlin-Heidelberg-New York: Springer 1972
[45] S.G.A. IV 1/2: Cohomologie étale: les points de départ, par P. Deligne, rédigé par J.F. Boutot. Lecture notes in Mathematics no 569. Berlin-Heidelberg-New York: Springer 1977
[46] Serre, J-P.: Corps locaux. Hermann, Act. Scient. et Ind., 1968
[47] Serre, J-P.: Cohomologie galoisienne. Lecture notes in Mathematics no. 5. Berlin-Heidelberg-New York: Springer 1964 · Zbl 0143.05901
[48] Serre, J-P.: Homologie singulière des espaces fibrés. Applications. Ann. of Maths. (2)54, 425-505 (1951) · Zbl 0045.26003
[49] Serre, J-P.: Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures). Séminaire Delange-Poitou-Pisot no 19, 1969/70
[50] Soulé, C.: Addendum to the article “On the torsion inK *(?)”. Duke Journal, pp. 131-132 (1978)
[51] Soulé, C.: Classes de torsion dans la cohomologie des groupes arithmétiques. C.R. Acad. Sc. Paris,284, 1009-1011 (1977) · Zbl 0346.55023
[52] Soulé, C.:K-théorie de ? et cohomologie étale. C.R. Acad. Sc. Paris,286, 1179-1181 (1978) · Zbl 0394.55004
[53] Soulé, C.: Groupes arithmétiques etK-théorie des anneaux d’entiers de corps de nombres. Thèse, Paris VII, 1978
[54] Tate, J.: Relations betweenK 2 and Galois cohomology. Inventiones Math.,36, 257-274 (1976) · Zbl 0359.12011 · doi:10.1007/BF01390012
[55] Tate, J.: Algebraic cycles and poles of zeta functions, dans “Arithmetical Algebraic Geometry” (O.F.G. Schilling ed.), p. 93, 1963
[56] Wagstaff, S.: The irregular primes to 125000. Math. Computations, p. 583, A.M.S. 1978 · Zbl 0377.10002
[57] Waldhausen, F.: AlgebraicK-theory of generalized free products, I et II. Annals of Maths.,108, 135-204, 205-256 (1978) · Zbl 0397.18012 · doi:10.2307/1971165
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