Arithmetic differential operators on a semistable model of ${\mathbb P}^1$

Deepam Patel; Tobias Schmidt; Matthias Strauch

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arXiv · 1410.1001

Arithmetic differential operators on a semistable model of ${\mathbb P}^1$

Deepam Patel·Tobias Schmidt·Matthias Strauch

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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.

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Deepam Patel, Tobias Schmidt, Matthias Strauch. 2014-10-04. Arithmetic differential operators on a semistable model of ${\mathbb P}^1$. https://arxiv.org/abs/1410.1001

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