On p-adic invariant cycles theorem
Chiarellotto, B; Coleman, R; Di Proietto, V; et al.Iovita, A
Date: 10 January 2014
Journal
Journal für die reine und angewandte Mathematik
Publisher
De Gruyter
Publisher DOI
Abstract
For a proper semistable curve X over a DVR of mixed characteristics we reprove the ”invariant
cycles theorem” with trivial coefficients (see [Ch99]) i.e. that the group of elements annihilated by the monodromy
operator on the first de Rham cohomology group of the generic fiber of X coincides with the first rigid cohomology
group of ...
For a proper semistable curve X over a DVR of mixed characteristics we reprove the ”invariant
cycles theorem” with trivial coefficients (see [Ch99]) i.e. that the group of elements annihilated by the monodromy
operator on the first de Rham cohomology group of the generic fiber of X coincides with the first rigid cohomology
group of its special fiber, without the hypothesis that the residue field of V is finite. This is done using the explicit
description of the monodromy operator on the de Rham cohomology of the generic fiber of X with coefficients
convergent F-isocrystals given in [CoIo10]. We apply these ideas to the case where the coefficients are unipotent
convergent F-isocrystals defined on the special fiber (without log-structure): we show that the invariant cycles
theorem does not hold in general in this setting. Moreover we give a sufficient condition for the non exactness.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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