Finiteness of rigid cohomology with coefficients

Duke Mathematical Journal

Volumn 134, Issue 1, 2006, Pages 15-97

  Kedlaya, Kiran S ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746866022     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-06-13412-9     Document Type: Article

References (55)

1. [A] Y. ANDRÉ, Filtrations de type Hasse-Arf et monodromie p-adique, Invent. Math. 148 (2002), 285-317. MR 1906151
2. [Ar] A. ARABIA, Relèvements des algèbres lisses et de leurs morphismes, Comment. Math. Helv. 76 (2001), 607-639. MR 1881700
3. [B1] P. BERTHELOT, Cohomologie cristalline des schémas de caractéristique p > 0, Lecture Notes in Math. 407, Springer, Berlin, 1974. MR 0384804
4. [B2] _, "Géométrie rigide et cohomologie des variétés algébriques de caractéristique p" in Introductions aux cohomologies p-adiques (Luminy, France, 1984), Mém. Soc. Math. France (N.S.) 23, Soc. Math. France, Montrouge, 1986, 7-32. MR 0865810
5. [B3] _, "Cohomologie rigide et théorie des script D sign-modules" in p-Adic Analysis (Trento, Italy, 1989), Lecture Notes in Math. 1454, Springer, Berlin, 1990, 80-124. MR 1094848
6. [B4] _, Dualité de Poincaré et formule de Künneth en cohomologie rigide, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), 493-498. MR 1692313
7. [B5] _, Finitude et pureté cohomologique en cohomologie rigide, Invent. Math. 128 (1997), 329-377. MR 1440308
8. [B6] _, "Introduction à la théorie arithmétique des script D sign-modules" in Cohomologies p-adiques et applications arithmétiques, II, Astérisque 279, Soc. Math. France, Montrouge, 2002, 1-80. MR 1922828
9. [B7] _, Cohomologie rigide et cohomologie rigide à supports propres: Première partie, preprint, 1996.
10. [BO] P. BERTHELOT and A. OGUS, Notes on Crystalline Cohomology, Princeton Univ. Press, Princeton, 1978. MR 0491705
11. [BGR] S. BOSCH, U. GÜNTZER, and R. REMMERT, Non-Archimedean Analysis: A Systematic Approach to Rigid Analytic Geometry, Grundlehren Math. Wiss. 261, Springer, Berlin, 1984. MR 0746961
12. [BT] R. BOTT and L. W. TU, Differential Forms in Algebraic Topology, Grad. Texts in Math. 82, Springer, New York, 1982. MR 0658304
13. [C] D. CARO, script D sign-modules arithmétiques surholonomes, preprint, 2005.
14. [CT] B. CHIARELLOTTO and N. TSUZUKI, Cohomological descent of rigid cohomology for étale coverings. Rend. Sem. Mat. Univ. Padova 109 (2003), 63-215. MR 1997987
15. [CM1] G. CHRISTOL and Z. MEBKHOUT, Sur le théorème de l'indice des équations différentielles p-adiques, III, Ann. of Math. (2) 151 (2000), 385-457. MR 1765703
16. [CM2] _, Sur le théorème de l'indice des équations différentielles p-adiques, IV, Invent. Math. 143 (2001), 629-672. MR 1817646
17. [Cr] R. CREW, Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve, Ann. Sci. École Norm. Sup. (4) 31 (1998), 717-763. MR 1664230
18. [dJ1] A. J. DE JONG, Smoothness, semi-stability and alterations, Inst. Hautes Études Sci. Publ. Math. 83 (1996), 51-93. MR 1423020
19. [dJ2] _, "Barsotti-Tate groups and crystals" in Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math. 1998, Extra Vol. II, Univ. Bielefeld, Bielefeld, Germany, 259-265. MR 1648076
20. [dJ3] _, Homomorphisms of Barsotti-Tate groups and crystals in positive characteristic, Invent. Math. 134 (1998), 301-333. MR 1650324
21. [D] P. DELIGNE, La conjecture de Weil, II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137-252. MR 0601520
22. [E] D. EISENBUD, Commutative Algebra: With a View toward Algebraic Geometry, Grad. Texts in Math. 150, Springer, New York, 1995. MR 1322960
23. [F] W. FULTON, A note on weakly complete algebras, Bull. Amer. Math. Soc. 75 (1969), 591-593. MR 0238829
24. [G] B. GRAY, Homotopy Theory: An Introduction to Algebraic Topology, Pure Appl. Math. 64, Academic Press, New York, 1975. MR 0402714
25. [GK1] E. GROSSE-KLÖNNE, Rigid analytic spaces with overconvergent structure sheaf, J. Reine Angew. Math. 519 (2000), 73-95. MR 1739729
26. [GK2] _, Finiteness of de Rham cohomology in rigid analysis. Duke Math. J. 113 (2002), 57-91. MR 1905392
27. [I] L. ILLUSIE, Complexe de de Rham-Witt et cohomologie cristalline, Ann. Sci. École Norm. Sup. (4) 12 (1979), 501-661. MR 0565469
28. [K1] K. S. KEDLAYA, Étale covers of affine spaces in positive characteristic, C. R. Math. Acad. Sci. Paris 335 (2002), 921-926. MR 1952550
29. [K2] _, Semistable reduction for overconvergent F-isocrystals on a curve, Math. Res. Lett. 10 (2003), 151-159. MR 1981892
30. [K3] _, A p-adic local monodromy theorem, Ann. of Math. (2) 160 (2004), 93 - 184. MR 2119719
31. [K4] _, Local monodromy of p-adic differential equations: An overview, Int. J. Number Theory 1 (2005), 109-154. MR 2172335
32. [K5] _, More étale covers of affine spaces in positive characteristic, J. Algebraic Geom. 14 (2005), 187-192. MR 2092132
33. [K6] _, Slope filtrations revisited, Doc. Math. 10 (2005), 447-525. MR2184462
34. [K7] _, Fourier transforms and p-adic "Weil II," preprint, arXiv:math.NT/0210149
35. [K8] _, Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensions, preprint, arXiv:math.NT/0405069
36. [Ki] R. KIEHL, Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie, Invent. Math. 2 (1967), 256-273. MR 0210949
37. [L] M. LAZARD, Les zéros des fonctions analytiques d'une variable sur un corps valué complet, Inst. Hautes Études Sci. Publ. Math. 14 (1962), 47-75. MR 0152519
38. [Lu] S. LUBKIN, Generalization of p-adic cohomology: Bounded Witt vectors. A canonical lifting of a variety in characteristic p ≠ 0 back to characteristic zero, Compositio Math. 34 (1977), 225-277. MR 0453745
39. [M1] Z. MEBKHOUT, Sur le théorème definitude de la cohomologie p-adique dune variété affine non singulière, Amer. J. Math. 119 (1997), 1027-1081. MR 1473068
40. [M2] _, Analogue p-adique du théorème de Turrittin et le théorème de la monodromie p-adique, Invent. Math. 148 (2002), 319-351. MR 1906152
41. [Mn] A. F. MONNA, Analyse non-archimédienne, Ergeb. Math. Grenzgeb. 56, Springer, Berlin, 1970. MR 0295033
42. [Mo] P. MONSKY, "One dimensional formal cohomology" in Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, Gauthier-Villars, Paris, 1971, 451-456. MR 0422279
43. [MW] P. MONSKY and G. WASHNITZER, Formal cohomology, 1, Ann. of Math. (2) 88 (1968), 181-217. MR 0248141
44. [O] A. OGUS, "The convergent topos in characteristic p" in The Grothendieck Festschrift, Vol. III, Progr. Math. 88, Birkhäuser, Boston, 1990, 133 -162. MR 1106913
45. [P] F. PHAM, Singularités de systèmes différentiels de Gauss-Manin, Progr. Math. 2, Birkhäuser, Boston, 1979. MR 0553954
46. [R] M. RAYNAUD, "Géométrie analytique rigide d'après Tate, Kiehl,...." in Table Ronde d'Analyse non archimédienne (Paris, 1972), Bull. Soc. Math. France Mem., no. 39-40, supplement to Bull. Soc. Math. France 102, Soc. Math. France, Montrouge, 1974, 319-327. MR 0470254
47. [S] P. SCHNEIDER, Nonarchimedean Functional Analysis, Springer Monogr. Math., Springer, Berlin, 2002. MR 1869547
48. [Sh] A. SHIHO, Crystalline fundamental groups, II: Log convergent cohomology and rigid cohomology, J. Math. Sci. Univ. Tokyo 9 (2002), 1-163. MR 1889223
49. [T1] N. TSUZUKI, Finite local monodromy of overconvergent unit-root F-isocrystals on a curve, Amer. J. Math. 120(1998), 1165-1190. MR 1657158
50. [T2] _, Slope filtration of quasi-unipotent overconvergent F-isocrystals, Ann. Inst. Fourier (Grenoble) 48 (1998), 379-412. MR 1625537
51. [T3] _, On the Gysin isomorphism of rigid cohomology, Hiroshima Math. J. 29 (1999), 479-527. MR 1728610
52. [T4] _, Morphisms of F-isocrystals and the finite monodromy theorem for unit-root F-isocrystals, Duke Math. J. 111 (2002), 385-418. MR 1885826
53. [T5] _, Cohomological descent of rigid cohomology for proper coverings, Invent. Math. 151 (2003), 101 - 133. MR 1943743
54. [T6] _, On base change theorem and coherence in rigid cohomology, Doc. Math. 2003, Extra Vol., 891-918. MR 2046617
55. [vdP] M. VAN DER PUT, "The cohomology of Monsky and Washnitzer" in Introductions aux cohomologies p-adiques (Luminy, France, 1984), Mem. Soc. Math. France (N.S.) 23, Soc. Math. France, Montrouge, 1986, 33-59. MR 0865811