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@article{Lazda:2019:10.1112/S0010437X19007164,
author = {Lazda, C and Pal, A},
doi = {10.1112/S0010437X19007164},
journal = {Compositio Mathematica},
pages = {1025--1045},
title = {Cycle classes in overconvergent rigid cohomology and a semistable Lefschetz (1,1) theorem},
url = {http://dx.doi.org/10.1112/S0010437X19007164},
volume = {155},
year = {2019}
}

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TY  - JOUR
AB  - 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.
AU  - Lazda,C
AU  - Pal,A
DO  - 10.1112/S0010437X19007164
EP  - 1045
PY  - 2019///
SN  - 0010-437X
SP  - 1025
TI  - Cycle classes in overconvergent rigid cohomology and a semistable Lefschetz (1,1) theorem
T2  - Compositio Mathematica
UR  - http://dx.doi.org/10.1112/S0010437X19007164
UR  - http://hdl.handle.net/10044/1/66935
VL  - 155
ER  -

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