The structure of Frobenius kernels for automorphism group schemes

Schröer, Stefan; Tziolas, Nikolaos

doi:10.2140/ant.2023.17.1637

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The structure of Frobenius kernels for automorphism group schemes

Stefan Schröer and Nikolaos Tziolas

Vol. 17 (2023), No. 9, 1637–1680

DOI: 10.2140/ant.2023.17.1637

Abstract

We establish structure results for Frobenius kernels of automorphism group schemes for surfaces of general type in positive characteristic. It turns out that there are surprisingly few possibilities. This relies on properties of the famous Witt algebra, which is a simple Lie algebra without finite-dimensional counterpart over the complex numbers, together with its twisted forms. The result actually holds true for arbitrary proper integral schemes under the assumption that the Frobenius kernel has large isotropy group at the generic point. This property is measured by a new numerical invariant called the foliation rank.

Keywords

automorphism group schemes, restricted lie algebras, surfaces of general type, foliations

Mathematical Subject Classification

Primary: 14L15, 14J50, 14G17, 14J29, 17B50, 13N15

Milestones

Received: 17 March 2022

Revised: 15 June 2022

Accepted: 18 August 2022

Published: 9 September 2023

Authors

Stefan Schröer
Mathematisches Institut Heinrich-Heine-Universität Düsseldorf Germany

Nikolaos Tziolas
Department of Mathematics and Statistics University of Cyprus Nicosia Cyprus

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Vol. 17, No. 9, 2023