Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Vanishing cycles
for non-archimedean analytic spaces


Author: Vladimir G. Berkovich
Journal: J. Amer. Math. Soc. 9 (1996), 1187-1209
MSC (1991): Primary 14F20, 32P05, 32S30
DOI: https://doi.org/10.1090/S0894-0347-96-00214-7
MathSciNet review: 1376692
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [Ber1] V. G. Berkovich, Spectral theory and analytic geometry over non-Archimedean fields, Mathematical Surveys and Monographs, vol. 33, Amer. Math. Soc., Providence, RI, 1990. MR 91k:32038
  • [Ber2] ------, Étale cohomology for non-Archimedean analytic spaces, Publ. Math. IHES 78 (1993), 5--161. MR 95c:14017
  • [Ber3] ------, Vanishing cycles for formal schemes, Invent. Math. 115 (1994), 539--571. MR 95f:14034
  • [Ber4] ------, On the comparison theorem for étale cohomology of non-Archimedean analytic spaces, Israel J. Math. 92 (1995), 45--60. CMP 96:03
  • [Bry] J. L. Brylinski, Un lemme sur les cycles évanescents en dimension relative 1, Ann. Scient. Éc. Norm. Sup. 19 (1986), 460--467.
  • [God] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1958. MR 21:1583
  • [EGA1] A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique. I. Le langage des schémas, Springer, Berlin-Heidelberg-New York, 1971. MR 36:177a; MR 29:1207
  • [EGA4] ------, Eléments de Géométrie Algébrique. IV. Étude local des schémas et des morphismes de schémas, Publ. Math. IHES, 20 (1964), 24 (1965), 28 (1966), 32 (1967). MR 30:3885; MR 33:7330; MR 36:178; MR 39:220
  • [Kel] J. L. Kelley, General Topology, D. Van Nostrand Company, Toronto-London-New York, 1955. MR 16:1136c
  • [Lau] G. Laumon, Charactéristique d'Euler-Poincaré et sommes exponentielles, Thése, Université de Paris-Sud, Orsay, 1983.
  • [SGA1] A. Grothendieck, Revêtements Étales et Groupe Fondamental, Lecture Notes in Math. 224, Springer, Berlin-Heidelberg-New York, 1971. MR 50:7129
  • [SGA4] M. Artin, A. Grothendieck, and J.-L. Verdier, Théorie des Topos et Cohomologie Étale des Schémas, Lecture Notes in Math. 269, 270, 305, Springer, Berlin-Heidelberg-New York, 1972--1973. MR 50:7130; MR 50:7131; MR 50:7132
  • [SGA4-1/2] P. Deligne et al., Cohomologie Étale, Lecture Notes in Math. 569, Springer, Berlin-Heidelberg-New York, 1977. MR 57:3132
  • [SGA7] A. Grothendieck, P. Deligne, and N. Katz, Groupes de Monodromie en Géométrie Algéb-rique, Lecture Notes in Math. 288, 340, Springer, Berlin-Heidelberg-New York, 1972--1973. MR 50:7134; MR 50:7135

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 14F20, 32P05, 32S30

Retrieve articles in all journals with MSC (1991): 14F20, 32P05, 32S30


Additional Information

Vladimir G. Berkovich
Affiliation: Department of Theoretical Mathematics, The Weizmann Institute of Science, P.O.B. 26, 76100 Rehovot, Israel
Email: vova@wisdom.weizmann.ac.il

DOI: https://doi.org/10.1090/S0894-0347-96-00214-7
Keywords: Algebraic geometry, \'{e}tale cohomology, $p$-adic analytic spaces
Received by editor(s): July 11, 1993
Additional Notes: The author is an Incumbent of the Reiter Family Career Development Chair.
Supported in part by NSF grant DMS-9100383.
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society