arXiv subjects

Efstathia Katsigianni

Publications and source records attributed to Efstathia Katsigianni.

2 recordsLinked to original sources

arXiv2018

Moduli of rank 1 isocrystals

In this article we express the set of rank 1 isocrystals on a proper curve as a subset of the de Rham moduli space, defined by Simpson and Langer. Using results from the theory of Berkovich spaces, we compare the $\ell$-adic cohomology of this subspace with the $\ell$-adic cohomology of the whole moduli space. This confirms a conjecture of Deligne in the rank 1 case and explains one of his examples in this case from the point of view of isocrystals.

math.AG↗

arXiv2018

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

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.

math.AG↗