no. 6
Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 6, pp. 717-763. 
@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},
     pages = {717--763},
     publisher = {Elsevier},
     volume = {Ser. 4, 31},
     number = {6},
     year = {1998},
     doi = {10.1016/s0012-9593(99)80001-9},
     mrnumber = {2000a:14023},
     zbl = {0943.14008},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(99)80001-9/}
}
TY  - JOUR
AU  - Crew, Richard
TI  - Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1998
SP  - 717
EP  - 763
VL  - 31
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(99)80001-9/
DO  - 10.1016/s0012-9593(99)80001-9
LA  - en
ID  - ASENS_1998_4_31_6_717_0
ER  - 
%0 Journal Article
%A Crew, Richard
%T Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
%J Annales scientifiques de l'École Normale Supérieure
%D 1998
%P 717-763
%V 31
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(99)80001-9/
%R 10.1016/s0012-9593(99)80001-9
%G en
%F 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, Série 4, Tome 31 (1998) no. 6, pp. 717-763. doi : 10.1016/s0012-9593(99)80001-9. http://www.numdam.org/articles/10.1016/s0012-9593(99)80001-9/

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

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

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

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

[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). | EuDML | Numdam | MR | Zbl

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

[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). | EuDML | Numdam | MR | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

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

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

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

[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 | Zbl

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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

[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 | Zbl

[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 | Zbl

[EVT] N. Bourbaki, Espaces vectoriels topologiques, Masson 1981, Paris. | MR | Zbl

[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 | Zbl

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

Cité par Sources :