Géométrie rigide et cohomologie des variétés algébriques de caractéristique
Mémoires de la Société Mathématique de France (1986)
- Volume: 23, page 7-32
- ISSN: 0249-633X
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topBerthelot, Pierre. "Géométrie rigide et cohomologie des variétés algébriques de caractéristique $p$." Mémoires de la Société Mathématique de France 23 (1986): 7-32. <http://eudml.org/doc/94864>.
@article{Berthelot1986,
author = {Berthelot, Pierre},
journal = {Mémoires de la Société Mathématique de France},
keywords = {rigid analytic cohomology; crystalline cohomology; Monsky-Washnitzer cohomology; overconvergent crystals},
language = {fre},
pages = {7-32},
publisher = {Société mathématique de France},
title = {Géométrie rigide et cohomologie des variétés algébriques de caractéristique $p$},
url = {http://eudml.org/doc/94864},
volume = {23},
year = {1986},
}
TY - JOUR
AU - Berthelot, Pierre
TI - Géométrie rigide et cohomologie des variétés algébriques de caractéristique $p$
JO - Mémoires de la Société Mathématique de France
PY - 1986
PB - Société mathématique de France
VL - 23
SP - 7
EP - 32
LA - fre
KW - rigid analytic cohomology; crystalline cohomology; Monsky-Washnitzer cohomology; overconvergent crystals
UR - http://eudml.org/doc/94864
ER -
References
top- [1] A. ADOLPHSON, S. SPERBER, Twisted Kloosterman sums and p-adic Bessel functions, Amer. Journ. of Math. 106, n° 3, 549-592 (1984). Zbl0552.12010MR85k:12002
- [2] P. BERTHELOT, Cohomologie cristalline des schémas de caractéristique p > 0, Lecture Notes in Math. 407, Springer Verlag (1974). Zbl0298.14012MR52 #5676
- [3] P. BERTHELOT, Cohomologie rigide et théorie de Dwork: le cas des sommes exponentielles, Astérisque 119-120, 17-49 (1984). Zbl0577.14013MR87b:14009
- [3 a] P. BERTHELOT, Cohomologie rigide et cohomologie rigide à support propre, en préparation.
- [4] P. BERTHELOT, A. OGUS, Notes on crystalline cohomology, Math. Notes 21, Princeton Univ. Press (1978). Zbl0383.14010MR58 #10908
- [5] P. BERTHELOT, A. OGUS, F-isocrystals and De Rham cohomology I, Inventiones Math. 72, 159-199 (1983). Zbl0516.14017MR85e:14025
- [6] B. DWORK, On the zeta function of a hypersurface: II, Annals of Math. 80, n° 2, 227-299 (1964). Zbl0173.48601MR32 #5654
- [7] B. DWORK, On the zeta function of a hypersurface: III, Annals of Math. 83, n° 3, 457-519 (1966). Zbl0173.48601MR35 #194
- [8] B. DWORK, On the zeta function of a hypersurface : IV. A deformation theory for singular hypersurfaces, Annals of Math. 90, n° 2, 335-352 (1969). Zbl0213.47402MR41 #8423
- [9] B. DWORK, p-adic cycles, Publ. Math. I.H.E.S. 37, 27-115 (1969). Zbl0284.14008MR45 #3415
- [10] B. DWORK, Bessel functions as p-adic functions of the argument, Duke Math. Journ. 41, 711-738 (1974). Zbl0302.14008MR52 #8124
- [11] R. ELKIK, Solutions d'équations à coefficients dans un anneau hensélien, Ann. Scient. Ec. Norm. Sup., 6, n° 4, 553-604 (1973). Zbl0327.14001MR49 #10692
- [12] J. FRESNEL, M. VAN DER PUT, Géométrie analytique rigide et applications, Progress in Math. 18, Birkhäuser (1981). Zbl0479.14015MR83g:32001
- [13] L. GERRITZEN, M. VAN DER PUT, Schottky groups and Mumford curves, Lecture Notes in Math. 817, Springer Verlag (1981). Zbl0442.14009MR82j:10053
- [14] R. HARTSHORNE, On the De Rham cohomology of algebraic varieties, Publ. Math. I.H.E.S. 45, 5-99 (1976). Zbl0326.14004MR55 #5633
- [15] L. ILLUSIE, Report on crystalline cohomology, Proc. of Symp. in pure Math. 29, 459-478 (1975). Zbl0326.14005MR52 #13845
- [16] L. ILLUSIE, Complexe de De Rham-Witt, Astérisque 63, 83-112 (1979). Zbl0446.14008MR81j:14012
- [17] L. ILLUSIE, Complexe de De Rham-Witt et cohomologie cristalline, Ann. Scient. Ec. Norm. Sup. 12, 501-661 (1979). Zbl0436.14007MR82d:14013
- [18] L. ILLUSIE, M. RAYNAUD, Les suites spectrales associées au complexe de De Rham-Witt, Publ. Math. I.H.E.S. 57, 73-212 (1983). Zbl0538.14012MR85e:14026
- [19] L. ILLUSIE, Finiteness, duality, and Künneth theorems in the cohomology of the De Rham-Witt complex, in "Algebraic Geometry", Lecture Notes in Math. 1016, 20-72 (1983). Zbl0538.14013MR85m:14033
- [20] N. KATZ, Travaux de Dwork, Séminaire Bourbaki 1971-72, exposé 409, Lecture Notes in Math. 317, 167-200, Springer Verlag (1973). Zbl0259.14007MR58 #16672
- [21] R. KIEHL, Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie, Inventiones Math. 2, 256-273 (1967). Zbl0202.20201MR35 #1834
- [22] S. LUBKIN, Finite generation of lifted p-adic homology with compact supports, Journ. of Number Theory 11, 412-464 (1979). Zbl0445.14011MR80h:14008
- [23] P. MONSKY, G. WASHNITZER, Formal cohomology: I, Annals of Math. 88, 181-217 (1968). Zbl0162.52504MR40 #1395
- [24] P. MONSKY, Formal cohomology : II, Annals of Math. 88, 218-238 (1968). Zbl0162.52601
- [25] P. MONSKY, Formal cohomology : III. Fixed point theorems, Annals of Math. 93, 315-343 (1971). Zbl0213.47501MR48 #296
- [26] A. OGUS, F-isocrystals and De Rham cohomology II, Duke Math. Journal 51, n° 4, p. 765-850 (1984). Zbl0584.14008MR86j:14012
- [27] M. RAYNAUD, Géométrie analytique rigide, Bull. Soc. Math. France, Mémoire 39, 40, 319-327 (1974). Zbl0299.14003MR57 #10012
- [28] P. ROBBA, Index of p-adic differential operators: III. Application to twisted exponential sums, Astérisque 119-120, p. 191-266 (1984). Zbl0548.12015MR86e:12011
- [29] S. SPERBER, p-adic hypergeometric functions and their cohomology, Duke Math. Journ. 44, 535-589 (1977). Zbl0408.12025MR57 #16307
- [30] S. SPERBER, Congruence properties of the hyperkloosterman sum, Compositio Mathematica 40, 3-33 (1980). Zbl0444.12014MR81j:10059
Citations in EuDML Documents
top- Nobuo Tsuzuki, Slope filtration of quasi-unipotent overconvergent -isocrystals
- Michel Gros, Luis Narváez-Macarro, Cohomologie évanescente -adique : calculs locaux
- Richard Crew, -isocrystals and their monodromy groups
- Bruno Chiarellotto, Nobuo Tsuzuki, Cohomological descent of rigid cohomology for étale coverings
- Nobuo TSUZUKI, A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties
- Michel Gros, Sur les -structures attachées aux courbes de Mumford
- G. Christol, Z. Mebkhout, Sur le théorème de l’indice des équations différentielles -adiques
- Richard Crew, Kloosterman sums and monodromy of a -adic hypergeometric equation
- Bruno Chiarellotto, Gilles Christol, On overconvergent isocrystals and -isocrystals of rank one
- A. J. De Jong, Crystalline Dieudonné module theory via formal and rigid geometry
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