Arithmetic differential operators on a semistable model of ${\mathbb P}^1$
Representation Theory
2014-10-08 v2 Number Theory
Abstract
In this paper we study sheaves of logarithmic arithmetic differential operators on a particular semistable model of the projective line. The main result here is that the first cohomology group of these sheaves is non-torsion. We also consider a refinement of the order filtration on the sheaf of level zero (before taking the p-adic completion). The associated graded sheaf, which we explicitly determine, explains to some extent the occurrence of the cohomology classes in degree one.
Cite
@article{arxiv.1410.1001,
title = {Arithmetic differential operators on a semistable model of ${\mathbb P}^1$},
author = {Deepam Patel and Tobias Schmidt and Matthias Strauch},
journal= {arXiv preprint arXiv:1410.1001},
year = {2014}
}
Comments
Added acknowledgement of support by the ANR program p-adic Hodge Theory and beyond (Th\'eHopaD)