A note on rank 1 log extendable isocrystals on simply connected open varieties

Efstathia Katsigianni

A note on rank 1 log extendable isocrystals on simply connected open varieties

Algebraic Geometry 2018-02-07 v2

Authors: Efstathia Katsigianni

Abstract

In 2010 de Jong proposed a $p$ -adic version of Gieseker's conjecture: if $X$ is a smooth, simply connected projective variety, then any isocrystal on $X$ is constant. This was proven by Esnault and Shiho under some additional assumptions. We show that the conjecture holds in the case of a non-proper variety with trivial tame fundamental group and for rank 1 log extendable isocrystals.

Keywords

p-adic Gieseker conjecture rank 1 log extendable isocrystals simply connected open varieties tame fundamental group non-proper varieties smooth projective varieties constant isocrystals

Cite

@article{arxiv.1703.04503,
  title  = {A note on rank 1 log extendable isocrystals on simply connected open varieties},
  author = {Efstathia Katsigianni},
  journal= {arXiv preprint arXiv:1703.04503},
  year   = {2018}
}

Comments

Major revision of the presentation. Reduced assumption to the triviality of the tame fundamental group. 18 pages. Comments very welcome!

A note on rank 1 log extendable isocrystals on simply connected open varieties

Abstract

Keywords

Cite

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