On the Euler-Poincaré characteristics of finite dimensional p -adic Galois representations

John Coates[1]; Ramdorai Sujatha[2]; Jean-Pierre Wintenberger[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

Publications Mathématiques de l'IHÉS (2001)

  • Volume: 93, page 107-143
  • ISSN: 0073-8301

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Coates, John, Sujatha, Ramdorai, and Wintenberger, Jean-Pierre. "On the Euler-Poincaré characteristics of finite dimensional $p$-adic Galois representations." Publications Mathématiques de l'IHÉS 93 (2001): 107-143. <http://eudml.org/doc/104173>.

@article{Coates2001,
affiliation = {DPMMS, University of Cambridge, Centre for Mathematical Sciences Wilberforce Road, Cambridge CB3 0WB; School of Mathematics, TIFR, Homi Bhabha Road Bombay 400 005, India; IRMA, Université Louis-Pasteur, 7, rue René-Descartes, F-67084 Strasbourg cedex, France},
author = {Coates, John, Sujatha, Ramdorai, Wintenberger, Jean-Pierre},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Galois representations; varieties over local ground fields; étale cohomology; motivic Galois representations; elliptic curves},
language = {eng},
pages = {107-143},
publisher = {Institut des Hautes Etudes Scientifiques},
title = {On the Euler-Poincaré characteristics of finite dimensional $p$-adic Galois representations},
url = {http://eudml.org/doc/104173},
volume = {93},
year = {2001},
}

TY - JOUR
AU - Coates, John
AU - Sujatha, Ramdorai
AU - Wintenberger, Jean-Pierre
TI - On the Euler-Poincaré characteristics of finite dimensional $p$-adic Galois representations
JO - Publications Mathématiques de l'IHÉS
PY - 2001
PB - Institut des Hautes Etudes Scientifiques
VL - 93
SP - 107
EP - 143
LA - eng
KW - Galois representations; varieties over local ground fields; étale cohomology; motivic Galois representations; elliptic curves
UR - http://eudml.org/doc/104173
ER -

References

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  1. [1] P. BERTHELOT, Cohomologie cristalline des schémas de caractéristique p | = 0 , Lecture Notes in Math. 407, Springer, 1974. Zbl0298.14012MR384804
  2. [2] A. BOREL, Linear algebraic groups, second edition, Graduate Texts in Math. 126, Springer, 1991. Zbl0726.20030MR1102012
  3. [3] N. BOURBAKI, Groupes et algèbres de Lie, Paris, Hermann, 1975. Zbl0483.22001MR453824
  4. [4] C. CHEVALLEY, S. EILENBERG, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124. Zbl0031.24803MR24908
  5. [5] B. CHIARELLOTTO, B. LE STUM, Sur la pureté de la cohomologie cristalline, C.R. Acad. Sci. Paris 326, Série I (1998), 961-963. Zbl0936.14016MR1649945
  6. [6] J. COATES, R. GREENBERG, Kummer theory for abelian varieties over local fields, Invent. Math. 124 (1996), 124-178. Zbl0858.11032MR1369413
  7. [7] J. COATES, S. HOWSON, Euler characteristics and elliptic curves II, Journal of Math. Society of Japan 53 (2001), 175-235. Zbl1046.11079MR1800527
  8. [8] J. COATES, R. SUJATHA, Euler-Poincaré characteristics of abelian varieties, C.R. Acad. Sci. Paris, 329, Série I (1999), 309-313. Zbl0967.14029MR1713337
  9. [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. Zbl0477.14004MR654325
  10. [10] M. DEMAZURE, P. GABRIEL, Groupes algébriques, tome I, North-Holland, 1970. Zbl0203.23401
  11. [11] G. FALTINGS, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366. Zbl0588.14026MR718935
  12. [12] G. FALTINGS, Crystalline cohomology and p-adic Galois representations, in: Algebraic analysis, geometry, and number theory, John Hopkins Univ. Press (1988), 25-80. Zbl0805.14008MR1463696
  13. [13] J.-M. FONTAINE, Modules galoisiens, modules filtrés et anneaux de Barsotti-Tate, Astérisque 65 (1979), 3-80. Zbl0429.14016MR563472
  14. [14] J.-M. FONTAINE, Représentations p-adiques semistables, in: Périodes p-adiques, Astérisque 223 (1994), 113-184. Zbl0865.14009MR1293972
  15. [15] H. GILLET, W. MESSING, Cycle classes and Riemann-Roch for crystalline cohomology, Duke Math. J. 55 (1987), 501-538. Zbl0651.14014MR904940
  16. [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. Zbl0811.14015MR1265522
  17. [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. Zbl0323.14010MR371902
  18. [18] N. KATZ, W. MESSING, Some consequences of the Riemann hypothesis for varieties over finite fields, Invent. Math. 23 (1974), 73-77. Zbl0275.14011MR332791
  19. [19] M. LAZARD, Groupes analytiques p-adiques, Publ. Math. IHES 26 (1965), 389-603. Zbl0139.02302MR209286
  20. [20] J. S. MILNE, Arithmetic Duality Theorems, Perspectives in Mathematics 1, Academic Press, 1986. Zbl0613.14019MR881804
  21. [21] R. PINK, l- adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture, J. Reine Angew. Math. 495 (1998), 187-237. Zbl0920.14006MR1603865
  22. [22] Groupes de monodromie en géométrie algébrique (SGA 7), exposé I, Lecture Notes in Math. 340, Springer, 1973. 
  23. [23] S. SEN, Lie algebras of Galois groups arising from Hodge-Tate modules, Ann. of Math. 97 (1973), 160-170. Zbl0258.12009MR314853
  24. [24] J.-P. SERRE, Sur la dimension cohomologique des groupes profinis, Topology 3 (1965), 413-420. Zbl0136.27402MR180619
  25. [25] J.-P. SERRE, Abelian l-adic representations and elliptic curves, Benjamin, 1968. Zbl0186.25701MR263823
  26. [26] J.-P. SERRE, Sur les groupes de congruence des variétés abéliennes II, Izv. Akad. Nauk. SSSR 35 (1971), 731-735. Zbl0222.14025MR289513
  27. [27] J.-P. SERRE, Représentations l-adiques, Kyoto Int. Symposium on Algebraic Number Theory (1977), 177-193 (= Collected Works II, 264-271). Zbl0406.14015MR476753
  28. [28] J.-P. SERRE, Groupes algébriques associés aux modules de Hodge-Tate, Astérisque 65 (1979), 159-188. Zbl0446.20028MR563476
  29. [29] J.-P. SERRE, Cohomologie galoisienne, 5e édition, Lecture Notes in Math. 5, Springer, 1994. Zbl0812.12002MR1324577
  30. [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. Zbl0943.20024
  31. [31] J. SILVERMAN, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Math. 151, Springer, 1995. Zbl0911.14015MR1312368
  32. [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). Zbl1028.22018MR1940683
  33. [33] J. TATE, Relations between K2 and Galois cohomology, Invent. Math. 36 (1976), 257-274. Zbl0359.12011MR429837
  34. [34] B. TOTARO, Euler characteristics for p-adic Lie groups, Publ. Math. IHES 90 (1999), 169-225. Zbl0971.22011MR1813226

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