Finite symplectic automorphism groups of supersingular K3 surfaces

TL;DR

This paper classifies all finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one, extending to all K3 surfaces in characteristic p>11.

Contribution

It provides a complete classification of finite symplectic automorphism groups on supersingular K3 surfaces and generalizes to all K3 surfaces in characteristic p>11.

Findings

Complete classification of symplectic automorphism groups for supersingular K3 surfaces of Artin invariant one.

Extension of classification to all K3 surfaces in characteristic p>11.

Utilizes work of Dolgachev and Keum for broader classification.

Abstract

We give a complete classification of finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one. Using work of Dolgachev and Keum, this provides the full classification of tame finite symplectic automorphism groups on any K3 surface, and in particular of all finite symplectic automorphism groups on K3 surfaces in characteristic p>11.