Cycle classes in overconvergent rigid cohomology and a semistable Lefschetz (1,1) theorem
File(s)
Accepted version
OA Location
Author(s)
Lazda, Chris
Pal, Ambrus
Type
Journal Article
Abstract
In this article we prove a semistable version of the variational Tate conjecture for divisors in crystalline cohomology, stating that a rational (logarithmic) line bundle on the special fibre of a semistable scheme over kJtK lifts to the total space if and only if its first Chern class does. The proof is elementary, using standard properties of the logarithmic de Rham–Witt complex. As a corollary, we deduce similar algebraicity lifting results for cohomology classes on varieties over global function fields. Finally, we give a counter-example to show that the variational Tate conjecture for divisors cannot hold with Qp-coefficients.
Date Issued
2019-05-01
Date Acceptance
2018-11-26
Citation
Compositio Mathematica, 2019, 155 (5), pp.1025-1045
ISSN
0010-437X
Publisher
London Mathematical Society
Start Page
1025
End Page
1045
Journal / Book Title
Compositio Mathematica
Volume
155
Issue
5
Copyright Statement
© The Authors 2019. The published version is located at https://doi.org/10.1112/S0010437X19007164
Subjects
Science & Technology
Physical Sciences
Mathematics
Picard groups
crystalline cohomology
semistable reduction
Tate conjecture
RHAM-WITT COHOMOLOGY
F-ISOCRYSTALS
REDUCTION
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2019-05-02