p-adic étale Tate twists and arithmetic duality
Sato, Kanetomo
Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007), p. 519-588 / Harvested from Numdam
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     author = {Sato, Kanetomo},
     title = {$p$-adic \'etale Tate twists and arithmetic duality},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {40},
     year = {2007},
     pages = {519-588},
     doi = {10.1016/j.ansens.2007.04.002},
     zbl = {pre05219874},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2007_4_40_4_519_0}
}
Sato, Kanetomo. $p$-adic étale Tate twists and arithmetic duality. Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007) pp. 519-588. doi : 10.1016/j.ansens.2007.04.002. http://gdmltest.u-ga.fr/item/ASENS_2007_4_40_4_519_0/

[1] Altman A., Kleiman S., Introduction to Grothendieck Duality Theory, Lecture Notes in Math., vol. 146, Springer, Berlin, 1970. | MR 274461 | Zbl 0215.37201

[2] Aritin M., Verdier J.-L., Seminar on étale cohomology of number fields, Woods Hole, 1964 characteristics.

[3] Bass H., Tate J., The Milnor ring of a global field, in: Bass H. (Ed.), Algebraic K-Theory II, Lecture Notes in Math., vol. 342, Springer, Berlin, 1972, pp. 349-446. | MR 442061 | Zbl 0299.12013

[4] Beilinson A.A., Height pairings between algebraic cycles, in: Manin Yu.I. (Ed.), K-Theory, Arithmetic and Geometry, Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 1-27. | MR 902590 | Zbl 0651.14002

[5] Beilinson A.A., Bernstein J., Deligne P., Faisceaux pervers, Astérisque, vol. 100, Soc. Math. France, 1982. | MR 751966 | Zbl 0536.14011

[6] Bloch S., Algebraic K-theory and crystalline cohomology, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 187-268. | Numdam | MR 488288 | Zbl 0388.14010

[7] Bloch S., Algebraic cycles and higher K-theory, Adv. Math. 61 (1986) 267-304. | MR 852815 | Zbl 0608.14004

[8] Bloch S., Esnault H., The coniveau filtration and non-divisibility for algebraic cycles, Math. Ann. 304 (1996) 303-314. | MR 1371769 | Zbl 0868.14004

[9] Bloch S., Kato K., p-adic étale cohomology, Inst. Hautes Études Sci. Publ. Math. 63 (1986) 107-152. | Numdam | MR 849653 | Zbl 0613.14017

[10] Bloch S., Ogus A., Gersten's conjecture and the homology of schemes, Ann. Sci. École Norm. Sup. (4) 7 (1974) 181-202. | Numdam | MR 412191 | Zbl 0307.14008

[11] Cassels J.W.S., Arithmetic on curves of genus 1 (IV). Proof of the Hauptvermutung, J. reine angew. Math. 211 (1962) 95-112. | MR 163915 | Zbl 0106.03706

[12] Deninger C., Duality in the étale cohomology of one-dimensional schemes and generalizations, Math. Ann. 277 (1987) 529-541. | MR 891590 | Zbl 0607.14011

[13] Fesenko I.B., Vostokov S.V., Local Fields and Their Extensions, with a Foreword by Shafarevich, I.R., Transl. Math. Monogr., vol. 121, second ed., Amer. Math. Soc., Providence, 2002. | MR 1915966 | Zbl 0781.11042

[14] Fontaine J.-M., Messing W., p-adic periods and p-adic étale cohomology, in: Ribet K.A. (Ed.), Current Trends in Arithmetical Algebraic Geometry, Contemp. Math., vol. 67, Amer. Math. Soc., Providence, 1987, pp. 179-207. | MR 902593 | Zbl 0632.14016

[15] Fujiwara K., A proof of the absolute purity conjecture (after Gabber), in: Usui S., Green M., Illusie L., Kato K., Looijenga E., Mukai S., Saito S. (Eds.), Algebraic Geometry 2000, Azumino, Adv. Stud. Pure Math., vol. 36, Math. Soc. Japan, Tokyo, 2002, pp. 153-183. | MR 1971516 | Zbl 1059.14026

[16] Gabber O., Some theorems on Azumaya algebras, in: Kervaire M., Ojanguren M. (Eds.), Groupe de Brauer Séminaire, Les Plans-sur-Bex, 1980, Lecture Notes in Math., vol. 844, Springer, Berlin, 1981, pp. 129-209. | MR 611868 | Zbl 0472.14013

[17] Geisser T., Motivic cohomology over Dedekind rings, Math. Z. 248 (2004) 773-794. | MR 2103541 | Zbl 1062.14025

[18] Gros M., Classes de Chern et classes des cycles en cohomologie logarithmique, Mém. Soc. Math. Fr. (N.S.) 21 (1985). | Numdam | Zbl 0615.14011

[19] Gros M., Suwa N., La conjecture de Gersten pour les faisceaux de Hodge-Witt logarithmique, Duke Math. J. 57 (1988) 615-628. | Zbl 0715.14011

[20] Grothendieck A., Le groupe de Brauer III, in: Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968, pp. 88-188. | MR 244271 | Zbl 0198.25901

[21] Hartshorne R., Residues and Duality, Lecture Notes in Math., vol. 20, Springer, Berlin, 1966. | MR 222093 | Zbl 0212.26101

[22] Hartshorne R., Local Cohomology, (a seminar given by Grothendieck, A., Harvard University, Fall, 1961), Lecture Notes in Math., vol. 41, Springer, Berlin, 1967. | MR 224620 | Zbl 0185.49202

[23] Hartshorne R., Algebraic Geometry, Grad. Texts in Math., vol. 52, Springer, New York, 1977. | MR 463157 | Zbl 0531.14001

[24] Hasse H., Die Gruppe der p n -primären Zahlen für einen Primteiler p von p, J. reine angew. Math. 176 (1936) 174-183. | JFM 62.1115.01

[25] Hyodo O., A note on p-adic étale cohomology in the semi-stable reduction case, Invent. Math. 91 (1988) 543-557. | MR 928497 | Zbl 0619.14013

[26] Hyodo O., On the de Rham-Witt complex attached to a semi-stable family, Compositio Math. 78 (1991) 241-260. | Numdam | Zbl 0742.14015

[27] Illusie L., Complexe de de Rham-Witt et cohomologie cristalline, Ann. Sci. École Norm. Sup. (4) 12 (1979) 501-661. | Numdam

[28] Illusie L., Réduction semi-stable ordinaire, cohomologie étale p-adique et cohomologie de de Rham d'après Bloch-Kato et Hyodo; Appendice à l'exposé IV, in: Périodes p-adiques, Séminaire de Bures, 1988, Astérisque, vol. 223, Soc. Math. France, Marseille, 1994, pp. 209-220. | Zbl 1043.11532

[29] Jannsen U., Saito S., Sato K., Étale duality for constructible sheaves on arithmetic schemes, http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/Jannsen/.

[30] Kato F., Log smooth deformation theory, Tôhoku Math. J. 48 (1996) 317-354. | MR 1404507 | Zbl 0876.14007

[31] Kato F., A generalization of local class field theory using K-groups, II, J. Fac. Sci. Univ. of Tokyo, Sec. IA 27 (1980) 602-683. | Zbl 0463.12006

[32] Kato F., On p-adic vanishing cycles (application of ideas of Fontaine-Messing), in: Algebraic Geometry, Sendai, 1985, Adv. Stud. in Pure Math., vol. 10, Kinokuniya, Tokyo, 1987, pp. 207-251. | Zbl 0645.14009

[33] Kato K., Logarithmic structures of Fontaine-Illusie, in: Igusa J. (Ed.), Algebraic Analysis, Geometry and Number Theory, The Johns Hopkins Univ. Press, Baltimore, 1988, pp. 191-224. | Zbl 0776.14004

[34] Kato K., The explicit reciprocity law and the cohomology of Fontaine-Messing, Bull. Soc. Math. France 119 (1991) 397-441. | Numdam | Zbl 0752.14015

[35] Kato K., Semi-stable reduction and p-adic étale cohomology, in: Périodes p-adiques, Séminaire de Bures, 1988, Astérisque, vol. 223, Soc. Math. France, Marseille, 1994, pp. 269-293. | MR 1293975 | Zbl 0847.14009

[36] Kato K., A Hasse principle for two-dimensional global fields (with an appendix by Colliot-Thélène, J.-L.), J. reine angew. Math. 366 (1986) 142-183. | MR 833016 | Zbl 0576.12012

[37] Katz N.M., Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Inst. Hautes Études Sci. Publ. Math. 39 (1970) 175-232. | Numdam | MR 291177 | Zbl 0221.14007

[38] Kurihara M., A note on p-adic étale cohomology, Proc. Japan Acad. Ser. A 63 (1987) 275-278. | MR 931263 | Zbl 0647.14006

[39] Langer A., Saito S., Torsion zero cycles on the self product of a modular elliptic curve, Duke Math. J. 85 (1996) 315-357. | MR 1417619 | Zbl 0880.14001

[40] Levine M., Techniques of localization in the theory of algebraic cycles, J. Algebraic Geom. 10 (2001) 299-363. | MR 1811558 | Zbl 1077.14509

[41] Levine M., K-theory and motivic cohomology of schemes, Preprint, 1999. | MR 1744925

[42] Lichtenbaum S., Duality theorems for curves over p-adic fields, Invent. Math. 7 (1969) 120-136. | MR 242831 | Zbl 0186.26402

[43] Lichtenbaum S., Values of zeta functions at non-negative integers, in: Jager H. (Ed.), Number Theory, Noordwijkerhout, 1983, Lecture Notes in Math., vol. 1068, Springer, Berlin, 1984, pp. 127-138. | MR 756089 | Zbl 0591.14014

[44] Lichtenbaum S., New results on weight-two motivic cohomology, in: Cartier P., Illusie L., Katz N.M., Laumon G., Manin Y., Ribet K.A. (Eds.), The Grothendieck Festschrift III, Progr. Math., vol. 88, Birkhäuser, Boston, 1990, pp. 35-55. | MR 1106910 | Zbl 0809.14004

[45] Mazur B., Notes on étale cohomology of number fields, Ann. Sci. École Norm. Sup. (4) 6 (1973) 521-552. | Numdam | MR 344254 | Zbl 0282.14004

[46] Milne J.S., Duality in flat cohomology of a surface, Ann. Sci. École Norm. Sup. (4) 9 (1976) 171-202. | Numdam | MR 460331 | Zbl 0334.14010

[47] Milne J.S., Values of zeta functions of varieties over finite fields, Amer. J. Math. 108 (1986) 297-360. | MR 833360 | Zbl 0611.14020

[48] Milne J.S., Arithmetic Duality Theorems, Perspectives in Math., vol. 1, Academic Press, Boston, 1986. | MR 881804 | Zbl 0613.14019

[49] Moser T., A duality theorem for étale p-torsion sheaves on complete varieties over finite fields, Compositio Math. 117 (1999) 123-152. | MR 1695861 | Zbl 0954.14012

[50] Niziol W., Duality in the cohomology of crystalline local systems, Compositio Math. 109 (1997) 67-97. | MR 1473606 | Zbl 0917.14010

[51] Poitou G., Cohomologie galoisienne des modules finis, Dunod, Paris, 1967. | MR 219591 | Zbl 0161.04203

[52] Raskind W., Abelian class field theory of arithmetic schemes, in: Jacob B., Rosenberg A. (Eds.), Algebraic K-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras (Part 1), Santa Barbara, 1992, Proc. Sympos. Pure Math., vol. 58, Amer. Math. Soc., Providence, 1995, pp. 85-187. | MR 1327282 | Zbl 0832.19004

[53] Saito S., Arithmetic on two-dimensional local rings, Invent. Math. 85 (1986) 379-414. | MR 846934 | Zbl 0609.13003

[54] Saito S., Arithmetic theory of arithmetic surfaces, Ann. of Math. 129 (1989) 547-589. | MR 997313 | Zbl 0688.14019

[55] Sato K., Logarithmic Hodge-Witt sheaves on normal crossing varieties, Math. Z., in press. | Zbl pre05208154

[56] Schneider P., p-adic point of motives, in: Jannsen U. (Ed.), Motives (Part 2), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, 1994, pp. 225-249. | MR 1265555 | Zbl 0814.14023

[57] Serre J.-P., Cohomologie galoisienne, Lecture Notes in Math., vol. 5, 5, Springer, Berlin, 1992. | Zbl 0812.12002

[58] Spiess M., Artin-Verdier duality for arithmetic surfaces, Math. Ann. 305 (1996) 705-792.

[59] Tate J., Duality theorems in the Galois cohomology of number fields, in: Proc. Internat. Congress Math., Stockholm, 1962, pp. 234-241. | Zbl 0126.07002

[60] Tate J., Algebraic cycles and poles of zeta functions, in: Schilling O.F.G. (Ed.), Arithmetical Algebraic Geometry, Harper and Row, New York, 1965, pp. 93-100. | MR 225778 | Zbl 0213.22804

[61] Tate J., On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, in: Séminaire Bourbaki 1965/66, Exposé 306, Benjamin, New York, 1966, and Collection Hors Série, Société mathématique de France, vol. 9, 1995. | Numdam | Zbl 0199.55604

[62] Thomason R.W., Absolute cohomological purity, Bull. Soc. Math. France 112 (1984) 397-406. | Numdam | MR 794741 | Zbl 0584.14007

[63] Tsuji T., p-adic étale cohomology and crystalline cohomology in the semi-stable reduction case, Invent. Math. 137 (1999) 233-411. | MR 1705837 | Zbl 0945.14008

[64] Tsuji T., On p-adic nearby cycles of log smooth families, Bull. Soc. Math. France 128 (2000) 529-575. | Numdam | MR 1815397 | Zbl 0972.14012

[65] Urabe T., The bilinear form of the Brauer group of a surface, Invent. Math. 125 (1996) 557-585. | MR 1400317 | Zbl 0871.13001

[66] Grothendieck A., Artin M., Verdier J.-L., Deligne P., Saint-Donat B., Théorie des topos et cohomologie étale des schémas, in: Lecture Notes in Math., vols. 269, 270, 305, Springer, Berlin, 1972, pp. 1972-1973. | MR 354654

[67] Deligne P., Boutot J.-F., Grothendieck A., Illusie L., Verdier J.-L., Cohomologie étale, Lecture Notes in Math., vol. 569, Springer, Berlin, 1977. | MR 463174 | Zbl 0345.00010