On the Euler-Poincaré characteristics of finite dimensional p-adic Galois representations
Publications Mathématiques de l'IHÉS, Volume 93 (2001), pp. 107-143.
Coates, John 1; Sujatha, Ramdorai 2; Wintenberger, Jean-Pierre 3

1 DPMMS, University of Cambridge, Centre for Mathematical Sciences Wilberforce Road, Cambridge CB3 0WB
2 School of Mathematics, TIFR, Homi Bhabha Road Bombay 400 005, India
3 IRMA, Université Louis-Pasteur, 7, rue René-Descartes, F-67084 Strasbourg cedex, France
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     title = {On the {Euler-Poincar\'e} characteristics of finite dimensional $p$-adic {Galois} representations},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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Coates, John; Sujatha, Ramdorai; Wintenberger, Jean-Pierre. On the Euler-Poincaré characteristics of finite dimensional $p$-adic Galois representations. Publications Mathématiques de l'IHÉS, Volume 93 (2001), pp. 107-143. http://archive.numdam.org/item/PMIHES_2001__93__107_0/

[1] P. Berthelot, Cohomologie cristalline des schémas de caractéristique p|=0, Lecture Notes in Math. 407, Springer, 1974. | MR | Zbl

[2] A. Borel, Linear algebraic groups, second edition, Graduate Texts in Math. 126, Springer, 1991. | MR | Zbl

[3] N. Bourbaki, Groupes et algèbres de Lie, Paris, Hermann, 1975. | MR | Zbl

[4] C. Chevalley, S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124. | MR | Zbl

[5] B. Chiarellotto, B. Le Stum, Sur la pureté de la cohomologie cristalline, C.R. Acad. Sci. Paris 326, Série I (1998), 961-963. | MR | Zbl

[6] J. Coates, R. Greenberg, Kummer theory for abelian varieties over local fields, Invent. Math. 124 (1996), 124-178. | MR | Zbl

[7] J. Coates, S. Howson, Euler characteristics and elliptic curves II, Journal of Math. Society of Japan 53 (2001), 175-235. | MR | Zbl

[8] J. Coates, R. Sujatha, Euler-Poincaré characteristics of abelian varieties, C.R. Acad. Sci. Paris, 329, Série I (1999), 309-313. | MR | Zbl

[9] P. DELIGNE, J. S. MILNE, Tannakian Categories in: P. Deligne, J. S. Milne, A. Ogus, K. Y. Shih (ed.), Hodge cycles, motives and Shimura varieties, Lecture notes in Math. 900, Springer, 1982. | MR | Zbl

[10] M. Demazure, P. Gabriel, Groupes algébriques, tome I, North-Holland, 1970. | Zbl

[11] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366. | EuDML | MR | Zbl

[12] G. Faltings, Crystalline cohomology and p-adic Galois representations, in: Algebraic analysis, geometry, and number theory, John Hopkins Univ. Press (1988), 25-80. | MR | Zbl

[13] J.-M. Fontaine, Modules galoisiens, modules filtrés et anneaux de Barsotti-Tate, Astérisque 65 (1979), 3-80. | MR | Zbl

[14] J.-M. Fontaine, Représentations p-adiques semistables, in: Périodes p-adiques, Astérisque 223 (1994), 113-184. | MR | Zbl

[15] H. Gillet, W. Messing, Cycle classes and Riemann-Roch for crystalline cohomology, Duke Math. J. 55 (1987), 501-538. | MR | Zbl

[16] L. Illusie, Crystalline cohomology, in: U. Jannsen, S. Kleiman, J.-P. Serre (ed.), Motives, Proc. Symp. Pure Math. 55, Part 1 (1994), 43-70. | MR | Zbl

[17] H. Imai, A remark on the rational points of abelian varieties with values in cyclotomic Zp-extensions, Proc. Japan. Acad. 51 (1971), 12-16. | MR | Zbl

[18] N. Katz, W. Messing, Some consequences of the Riemann hypothesis for varieties over finite fields, Invent. Math. 23 (1974), 73-77. | EuDML | MR | Zbl

[19] M. Lazard, Groupes analytiques p-adiques, Publ. Math. IHES 26 (1965), 389-603. | EuDML | Numdam | MR | Zbl

[20] J. S. Milne, Arithmetic Duality Theorems, Perspectives in Mathematics 1, Academic Press, 1986. | MR | Zbl

[21] R. Pink, l- adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture, J. Reine Angew. Math. 495 (1998), 187-237. | MR | Zbl

[22] Groupes de monodromie en géométrie algébrique (SGA 7), exposé I, Lecture Notes in Math. 340, Springer, 1973.

[23] S. Sen, Lie algebras of Galois groups arising from Hodge-Tate modules, Ann. of Math. 97 (1973), 160-170. | MR | Zbl

[24] J.-P. Serre, Sur la dimension cohomologique des groupes profinis, Topology 3 (1965), 413-420. | MR | Zbl

[25] J.-P. Serre, Abelian l-adic representations and elliptic curves, Benjamin, 1968. | MR | Zbl

[26] J.-P. Serre, Sur les groupes de congruence des variétés abéliennes II, Izv. Akad. Nauk. SSSR 35 (1971), 731-735. | MR | Zbl

[27] J.-P. Serre, Représentations l-adiques, Kyoto Int. Symposium on Algebraic Number Theory (1977), 177-193 (= Collected Works II, 264-271). | MR | Zbl

[28] J.-P. Serre, Groupes algébriques associés aux modules de Hodge-Tate, Astérisque 65 (1979), 159-188. | MR | Zbl

[29] J.-P. Serre, Cohomologie galoisienne, 5e édition, Lecture Notes in Math. 5, Springer, 1994. | MR | Zbl

[30] J.-P. Serre, La distribution d'Euler-Poincaré d'un groupe profini, in A. J. Scholl and R. L. Taylor (ed.), Galois representations in Arithmetic Algebraic Geometry, Cambridge Univ. Press (1998), 461-493. | Zbl

[31] J. Silverman, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Math. 151, Springer, 1995. | MR | Zbl

[32] R. Sujatha, Euler-Poincaré characteristics of p-adic Lie groups and arithmetic, Proceedings of the International Conference on Algebra, Arithmetic and Geometry TIFR (2000), (to appear). | MR | Zbl

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

[34] B. Totaro, Euler characteristics for p-adic Lie groups, Publ. Math. IHES 90 (1999), 169-225. | EuDML | Numdam | MR | Zbl