Professor Vladimir Berkovich
Department of Mathematics
Ziskind Building, Room 257
Weizmann Institute of Science
P.O.B. 26, Rehovot 76100, Israel

Tel: +972-8-934-3216
Fax: +972-8-934-4308


Vladimir Berkovich

Research Interests

Selected Publications

* The marked files may be slightly different from the published versions, e.g., they may not include corrections made to the proofs.

Complex analytic vanishing cycles for formal schemes
May, 2015 (revised on July 1, 2018).
PDF 1.1 MB
Finiteness theorems for vanishing cycles of formal schemes
Israel J. Math. 210 (2015), 147-191.
PDF 491 KB
A non-Archimedean interpretation of the weight zero subspaces of limit mixed Hodge structures
in Algebra, Arithmetic and Geometry. Volume I: In Honor of Y.I. Manin,
Progress in Mathematics, vol. 269, Birkhäuser Boston, 2010, 49-67.
PDF *273 KB
Non-archimedean analytic geometry: first steps
in p-adic Geometry: Lectures from the 2007 Arizona Winter School,
University Lecture Series, vol. 45, American Mathematical Society, Providence, R.I., 2008, 1-7.
PDF 124 KB
Integration of One-forms on P-adic Analytic Spaces
Annals of Mathematics Studies 162, Princeton University Press, Princeton and Oxford, 2006, 156 pp.
*900 KB
Smooth p-adic analytic spaces are locally contractible. II
in Geometric Aspects of Dwork Theory, Walter de Gruyter & Co., Berlin, 2004, 293-370.
PDF 584 KB
A result on vanishing cycles
Appendix to Harris, M.; Taylor, R.: The Geometry and Cohomology of Some Simple Shimura Varieties,
Annals of Mathematics Studies 151, Princeton University Press, Princeton and Oxford, 2001, 257-260.
PDF *99 KB
An analog of Tate's conjecture over local and finitely generated fields
Internat. Math. Res. Notices 2000, no. 13, 665-680.
PDF 171 KB
Smooth p-adic analytic spaces are locally contractible
Invent. Math. 137 (1999), no. 1, 1-84.
PDF 692 KB
p-Adic Analytic Spaces
in Proceedings of the International Congress of Mathematicians, Berlin, August 1998,
Doc. Math. J. DMV, Extra Volume ICM II (1998), 141-151.
PDF 173 KB
Vanishing cycles for formal schemes. II
Invent. Math. 125 (1996), no. 2, 367-390.
PDF 467 KB
Vanishing cycles for non-Archimedean analytic spaces
J. Amer. Math. Soc. 9 (1996), no. 4, 1187-1209.
PDF 533 KB
The automorphism group of the Drinfeld half-plane
C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 9, 1127-1132.
PDF *150 KB
On the comparison theorem for étale cohomology of non-Archimedean analytic spaces
Israel J. Math. 92 (1995), 45-60.
PDF 644 KB
Vanishing cycles for formal schemes
Invent. Math. 115 (1994), no. 3, 539-571.
PDF 1.8 MB
Étale cohomology for non-Archimedean analytic spaces
Publ. Math. IHES 78 (1993), 5-161.
Spectral theory and analytic geometry over non-Archimedean fields
Mathematical Surveys and Monographs, vol. 33, American Mathematical Society, Providence, RI, 1990, 169 pp.
AMS $57, $71

Notes and videos of lectures

Complex analytic vanishing cycles for formal schemes
Video of a talk at the Joint IAS/PU Number Theory Seminar
Institute for Advanced Study, Princeton, December 12, 2013
MP4 Link
Integration of one-forms on p-adic analytic spaces
Notes of a talk at the Simons Simposium on non-Archimedean and tropical geometry
St. John, US Virgin Islands, April 1 - 5, 2013
PDF 243 KB
Analytic geometry over F1
Slides of a talk at the conference on the occasion of Francesco Baldassarri’s 60th birthday
Padova, February 3 - 5, 2011
PDF 583 KB
Algebraic geometry over F1
Videos of four lectures at the Summer school on Berkovich spaces
Institut de Mathématiques de Jussieu, Paris, June 28 - July 10, 2010
MOV Link
Non-archimedean analytic spaces
Notes of lectures at the Advanced School on p-adic Analysis and Applications
ICTP, Trieste, August 31 - September 11, 2009
PDF 323 KB

Unfinished projects

Analytic geometry over F1
PDF 922 KB
Algebraic geometry over F1
PDF 919 KB
Étale equivariant sheaves on p-adic analytic spaces
PDF 182 KB

Faculty of Mathematics And Computer Science

Weizmann Institute of Science