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Arithmetic differential operators on a semistable model of $${\mathbb {P}}^1$$P1

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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… Click to show full 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 contains a non-torsion element. This shows that the model is not D-affine for such differential operators.

Keywords: semistable model; arithmetic differential; operators semistable; differential; differential operators

Journal Title: Mathematische Zeitschrift
Year Published: 2018

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