Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
Crew, Richard
Annales scientifiques de l'École Normale Supérieure, Tome 31 (1998), p. 717-763 / Harvested from Numdam
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@article{ASENS_1998_4_31_6_717_0,
     author = {Crew, Richard},
     title = {Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {31},
     year = {1998},
     pages = {717-763},
     doi = {10.1016/s0012-9593(99)80001-9},
     mrnumber = {2000a:14023},
     zbl = {0943.14008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1998_4_31_6_717_0}
}

Crew, Richard. Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve. Annales scientifiques de l'École Normale Supérieure, Tome 31 (1998) pp. 717-763. doi : 10.1016/s0012-9593(99)80001-9. http://gdmltest.u-ga.fr/item/ASENS_1998_4_31_6_717_0/

[1] A. Adolphson, An index theorem for p-adic differential operators, (Trans. AMS, Vol. 216, 1976, pp. 279-293). | MR 387284 | MR 52 #8127 | Zbl 0297.47039

[2] E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, Geometry of Algebraic Curves, Volume I, Springer, 1985. | MR 770932 | MR 86h:14019 | Zbl 0559.14017

[3] P. Berthelot, Cohomologie cristalline des schémas de caractéristique p > 0, (Lecture Notes in Math., Vol. 407, Springer 1974). | MR 384804 | MR 52 #5676 | Zbl 0298.14012

[4] P. Berthelot, Cohomologie rigide et théorie de Dwork : le cas des sommes exponentielles, (Astérisque, Vol. 119-120, 1984, pp. 17-49). | MR 773087 | MR 87b:14009 | Zbl 0577.14013

[5] P. Berthelot, Géométrie rigide et cohomologie des variétés algébriques de caracteristique p, (Journées d'analyse p-adique (Luminy 1982), Mémoire de la S.M.F. n° 23, suppl. au Bull. S.M.F., Vol. 114, 1986, fasc. 2, pp. 7-32). | Numdam | MR 865810 | MR 88a:14020 | Zbl 0606.14017

[6] P. Berthelot, Cohomologie rigide et théorie des D-modules, (in Lecture Notes in Math., Vol. 1454, Springer 1990). | MR 1094848 | MR 92h:14013 | Zbl 0722.14008

[7] P. Berthelot, D-Modules arithmétiques I. Opérateurs différentielles de niveau fini, (Annales Sc. Ec. Norm. Sup. 4e ser., Vol. 29, 1996, pp. 185-272). | Numdam | MR 1373933 | MR 97b:14019 | Zbl 0886.14004

[8] P. Berthelot, Cohomologie rigide et cohomologie rigide à support propre, preprint IRMAR.

[9] P. Berthelot, Finitude et pureté cohomologique en cohomologie rigide, (Inv. Math., Vol. 128, 1997, pp. 329-377). | MR 1440308 | MR 98j:14023 | Zbl 0908.14005

[10] B. Chiarellotto, Duality in rigid analysis, (in Lecture Notes in Math., Vol. 1454, Springer 1990). | MR 92d:32015 | Zbl 0737.32012

[11] G. Christol, Un théorème de transfert pour les disques singuliers réguliers, (Astérisque, Vol. 119-120, 1984, pp. 151-168). | MR 86h:12012 | Zbl 0553.12014

[12] G. Christol and Z. Mebkhout, Sur le théorème de l'indice des équations différentielles p-adiques II, (Annals of Math.). | Zbl 0929.12003

[13] G. Christol and Z. Mebkhout, Sur le théorème de l'indice des équations différentielles p-adiques III, preprint.

[14] R. Crew, F-isocrystals and p-adic representations, (Proc. Symp. Pure Math., Vol. 46, 1987, pp. 111-138). | MR 89c:14024 | Zbl 0639.14011

[15] R. Crew, F-isocrystals and their monodromy groups, (Annales Sc. Ec. Norm. Sup. 4e ser., Vol. 25, 1992, pp. 429-464). | Numdam | MR 94a:14021 | Zbl 0783.14008

[16] R. Crew, Kloosterman sums and the monodromy of a p-adic hypergeometric equation, (Compositio Mathematica, Vol. 91, 1994, pp. 1-36). | Numdam | MR 95h:11082 | Zbl 0806.14018

[17] P. Deligne, La conjecture de Weil II, (Publ. Math. IHES, Vol. 52, 1980, pp. 137-252). | Numdam | MR 83c:14017 | Zbl 0456.14014

[18] B. Dwork, On the zeta function of a hypersurface, (Publ. Math IHES, Vol. 12, 1962, pp. 5-68 ; II, Annals of Math., Vol. 80, n° 2, 1964, pp. 227-299 ; III, Annals of Math., Vol. 83, n° 3, 1966, pp. 457-519 ; IV. A deformation theory for singular hypersurfaces, Annals of Math., Vol. 90, n° 2, 1969, pp. 335-352).

[19] P. Enflo, A counterexample to approximation problem in Banach spaces, (Acta Mathematica, Vol. 130, 1973, pp. 309-317). | MR 53 #6288 | Zbl 0267.46012

[20] G. Faltings, F-isocrystals on open varieties, results and conjectures, in The Grothendieck Festschrift vol. 2, Birkhauser, 1990. | MR 92f:14015 | Zbl 0736.14004

[21] J. Fresnel and M. Van Der Put, Géométrie analytique rigide et applications, Birkhauser 1981. | MR 83g:32001 | Zbl 0479.14015

[22] W. Fulton, A note on weakly complete algebras, (Bull. AMS, Vol. 75, 1969, pp. 591-593). | MR 39 #193 | Zbl 0205.34303

[23] L. Gruson, Catégories d'espaces de Banach ultramétriques, (Bul. Sc. Math. 2e ser., Vol. 91, 1966, pp. 287-299). | Numdam | MR 36 #1957 | Zbl 0149.34801

[24] N. Katz, On the calculation of some differential galois groups, (Inv. Math., Vol. 87, 1987, pp. 13-61). | MR 88c:12010 | Zbl 0609.12025

[25] H. Komatsu, Projective and injective limits of weakly compact sequences of locally convex spaces, (J. Math. Soc. Japan, Vol. 19, 1967, pp. 366-383). | MR 36 #646 | Zbl 0168.10603

[26] M. Lazard, Les zéros d'une fonction analytique d'une variable sur un corps valué complet, (Publ. Math. IHES, Vol. 14, 1962). | Numdam | MR 27 #2497 | Zbl 0119.03701

[27] B. Le Stum, Applications of rigid cohomology to arithmetic geometry, (Thesis, Univ. of Minnesota, 1988).

[28] Z. Mebhout, Sur le théorème de finitude de la cohomologie p-adique d'une variété affine non-singulière, (American J. Math, Vol. 119, no. 5, 1997, pp. 1127-1082). | MR 99a:14027 | Zbl 0926.14007

[29] A. Monna, Analyse non-archimédienne, Springer 1970. | MR 45 #4101 | Zbl 0203.11501

[30] P. Monsky and G. Washnitzer, Formal cohomology : I, (Annals of Math., Vol. 88, 1968, pp. 181-217). | MR 40 #1395 | Zbl 0162.52504

[31] P. Monsky, Formal cohomology : II, (Annals of Math., Vol. 88, 1968, pp. 218-238 ; III : Fixed point theorems, (Annals of Math., Vol. 93, 1971, pp. 315-343). | MR 40 #1395 | Zbl 0213.47501

[32] Y. Morita, A p-adic theory of hyperfunctions I, (RIMS Publ., Vol. 17, No. 1, 1981, pp. 1-24). | MR 84b:12025 | Zbl 0457.12010

[33] D. Reich, A p-adic fixed point formula, (Amer. J. Math., Vol. 91, 1969, pp. 835-850). | MR 41 #210 | Zbl 0213.47502

[34] J.-P. Serre, Endomorphismes complètement continus des espaces de Banach, (Publ. Math. IHES, Vol. 12, 1962, pp. 69-85). | Numdam | MR 26 #1733 | Zbl 0104.33601

[35] J.-P. Serre, Groupes algébriques et corps de classes, Hermann 1959, Paris. | MR 21 #1973 | Zbl 0097.35604

[36] N. Tsuzuki, The overconvergence of morphisms of étale Ø-∇-spaces on a local field, preprint.

[37] N. Tsuzuki, Finite monodromy of p-adic representations on a local field of positive characteristic, preprint.

[38] M. Van Der Put, Serre duality for rigid spaces, (Indag. Math. N.S., Vol. 3, (2), 1992, pp. 219-235). | MR 93d:32054 | Zbl 0762.32016

[39] J. Van Tiel, Espaces localement K-convexes I, (Proc. Kon. Ned. Akad. v. Wetensch., Vol. 69, 1965, pp. 249-258, II, pp. 259-272, III, pp. 273-289). | MR 31 #3841a | Zbl 0133.06502

[EVT] N. Bourbaki, Espaces vectoriels topologiques, Masson 1981, Paris. | MR 83k:46003 | Zbl 0482.46001

[AC] N. Bourbaki, Algèbre commutative, Masson 1985, Paris.

[TG] N. Bourbaki, Topologie générale.

[CE] H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press 1956. | MR 17,1040e | Zbl 0075.24305

[EGA] A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, (Publ. Math. IHES, Vol. 4, 8, 11, 17, 20, 24, 28, 32). | Numdam