The Representations of the Automorphism Groups and the Frobenius Invariants of K3 Surfaces

摘要

For a complex algebraic K3 surface, it is known that the representations of the automorphism group on the transcendental cycles is finite and is isomorphic to the representation on the two-forms. In this paper, we prove similar results for a K3 surface defined over a field of odd characteristic. Also, we prove that the height and the Artin invariant of a K3 surface equipped with a nonsymplectic automorphism of some high order are determined by a congruence class of the base characteristic.