Étale cohomology for non-Archimedean analytic spaces

Vladimir G. Berkovich

Publications Mathématiques de l'IHÉS (1993)

  • Volume: 78, page 5-161
  • ISSN: 0073-8301

How to cite

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Berkovich, Vladimir G.. "Étale cohomology for non-Archimedean analytic spaces." Publications Mathématiques de l'IHÉS 78 (1993): 5-161. <http://eudml.org/doc/104093>.

@article{Berkovich1993,
author = {Berkovich, Vladimir G.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {étale cohomology; compact support; analytic spaces; morphisms; sheaves; rigid spaces},
language = {eng},
pages = {5-161},
publisher = {Institut des Hautes Études Scientifiques},
title = {Étale cohomology for non-Archimedean analytic spaces},
url = {http://eudml.org/doc/104093},
volume = {78},
year = {1993},
}

TY - JOUR
AU - Berkovich, Vladimir G.
TI - Étale cohomology for non-Archimedean analytic spaces
JO - Publications Mathématiques de l'IHÉS
PY - 1993
PB - Institut des Hautes Études Scientifiques
VL - 78
SP - 5
EP - 161
LA - eng
KW - étale cohomology; compact support; analytic spaces; morphisms; sheaves; rigid spaces
UR - http://eudml.org/doc/104093
ER -

References

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  1. [Ber] BERKOVICH, V. G., Spectral theory and analytic geometry over non-Archimedean fields, Mathematical Surveys and Monographs, vol. 33, American Mathematical Society, 1990. Zbl0715.14013MR91k:32038
  2. [Bos] BOSCH, S., Eine bemerkenswerte Eigenschaft der formellen Fasern affinoider Räume, Math. Ann., 229 (1977), 25-45. Zbl0385.32008MR56 #5952
  3. [BGR] BOSCH, S., GÜNTZER, U., Remmert, R., Non-Archimedean analysis. A systematic approach to rigid analytic geometry, Grundlehren der Mathematischen Wissenschaften, Bd. 261, Springer, Berlin-Heidelberg-New York, 1984. Zbl0539.14017
  4. [BL] BOSCH, S., LÜTKEBOHMERT, W., Stable reduction and uniformization of abelian varieties I, Math. Ann., 270 (1985), 349-379. Zbl0554.14012MR86j:14040a
  5. [Bou] BOURBAKI, N., Topologie générale, Paris, Hermann, 1951. 
  6. [Car] CARAYOL, H., Non-abelian Lubin-Tate Theory, in Automorphic Forms, Shimura Varieties, and L-Functions, New York-London, Academic Press, 1990, 15-39. Zbl0704.11049MR91i:11169
  7. [Dr1] DRINFELD, V. G., Elliptic modules, Math. USSR Sbornik, 23 (1974), 561-592. Zbl0321.14014MR52 #5580
  8. [Dr2] DRINFELD, V. G., Coverings of p-adic symmetric domains, Funct. Anal. Appl., 10 (1976), 107-115. Zbl0346.14010MR54 #10281
  9. [En] ENGELKING, R., General topology, Warszawa, 1977. Zbl0373.54002MR58 #18316b
  10. [FrPu] FRESNEL, J., VAN DER PUT, M., Géométrie analytique rigide et applications, Progress in Mathematics, vol. 18, Boston, Birkhäuser, 1981. Zbl0479.14015MR83g:32001
  11. [GaZi] GABRIEL, P., ZISMAN, M., Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 35, Berlin-Heidelberg-New York, Springer, 1967. Zbl0186.56802MR35 #1019
  12. [God] GODEMENT R., Topologie algébrique et théorie des faisceaux, Paris, Hermann, 1958. Zbl0080.16201MR21 #1583
  13. [Gro] GROTHENDIECK, A., Sur quelques points d'algèbre homologique, Tôhoku Math. J., 9 (1957), 119-221. Zbl0118.26104MR21 #1328
  14. [Gro2] GROTHENDIECK, A., Le groupe de Brauer, in Dix exposés sur la cohomologie des schémas, Amsterdam, North-Holland, 1968, 46-188. Zbl0198.25901MR39 #5586a
  15. [EGAIV] GROTHENDIECK, A., DIEUDONNÉ, J., Éléments de géométrie algébrique, IV. Étude locale des schémas et des morphismes de schémas, Publ. Math. I.H.E.S., 20 (1964), 25 (1965), 28 (1966), 32 (1967). Zbl0136.15901
  16. [Gru] GRUSON, L., Théorie de Fredholm p-adique, Bull. Soc. math. France, 94 (1966), 67-95. Zbl0149.34702MR37 #1971
  17. [Ha1] HARTSHORNE, R., Residues and Duality, Lecture Notes in Math., 20, Berlin-Heidelberg-New York, Springer, 1966. Zbl0212.26101MR36 #5145
  18. [Ha2] HARTSHORNE, R., Algebraic Geometry, Berlin-Heidelberg-New York, Springer, 1977. Zbl0367.14001MR57 #3116
  19. [Kie] KIEHL, R., Ausgezeichnete Ringe in der nichtarchimedischen analytischen Geometrie, J. Reine Angew. Math., 234 (1969), 89-98. Zbl0169.36501MR39 #4450
  20. [Mat] MATSUMURA, H., Commutative ring theory, Cambridge University Press, 1980. 
  21. [Mit] MITCHELL, B., Theory of Categories, New York-London, Academic Press, 1965. Zbl0136.00604MR34 #2647
  22. [Put] VAN DER PUT, M., The class group of a one-dimensional affinoid space, Ann. Inst. Fourier, 30 (1980), 155-164. Zbl0426.14014MR82h:14018
  23. [Ray] RAYNAUD, M., Anneaux locaux henséliens, Lecture Notes in Math., 169, Berlin-Heidelberg-New York, Springer, 1970. Zbl0203.05102MR43 #3252
  24. [SGA1] GROTHENDIECK, A., Séminaire de géométrie algébrique, I. Revêtements étales et groupe fondamental, Lecture Notes in Math., 224, Berlin-Heidelberg-New York, Springer, 1971. Zbl0234.14002MR50 #7129
  25. [SGA4] ARTIN, M., GROTHENDIECK, A., VERDIER, J.-L., Théorie des topos et cohomologie étale des schémas, Lecture Notes in Math., 269, 270, 305, Berlin-Heidelberg-New York, Springer, 1972-1973. 
  26. [SGA41/2] DELIGNE, P. et al., Cohomologie étale, Lectures Notes in Math., 569, Berlin-Heidelberg-New York, Springer, 1977. Zbl0345.00010MR57 #3132
  27. [ScSt] SCHNEIDER, P., STUHLER, U., The cohomology of p-adic symmetric spaces, Invent. math., 105 (1991), 47-122. Zbl0751.14016MR92k:11057
  28. [Ser] SERRE, J.-P., Cohomologie galoisienne, Lectures Notes in Math., 5, Berlin-Heidelberg-New York, Springer, 1964. Zbl0128.26303
  29. [ZaSa] ZARISKI, O., SAMUEL, P., Commutative algebra, Berlin-Heidelberg-New York, Springer, 1975. 

Citations in EuDML Documents

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  1. Antoine Ducros, Image réciproque du squelette par un morphisme entre espaces de Berkovich de même dimension
  2. A. J. De Jong, Étale fundamental groups of non-archimedean analytic spaces
  3. Yakov Varshavsky, p -adic uniformization of unitary Shimura varieties
  4. Antoine Ducros, Les espaces de Berkovich sont excellents
  5. Thomas Hausberger, Uniformisation des variétés de Laumon-Rapoport-Stuhler et conjecture de Drinfeld-Carayol
  6. Elena Mantovan, On non-basic Rapoport-Zink spaces
  7. Jean-François Boutot, Uniformisation p -adique des variétés de Shimura
  8. William Gignac, Equidistribution of preimages over nonarchimedean fields for maps of good reduction
  9. Brian Conrad, Relative ampleness in rigid geometry
  10. Jean François Dat, Espaces symétriques de Drinfeld et correspondance de Langlands locale

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