Recognizing Galois representations of K3 surfaces

TL;DR

This paper proposes a criterion, based on major conjectures, to identify when a compatible system of l-adic representations corresponds to the second cohomology of a K3 surface, linking abstract Galois representations to geometric objects.

Contribution

It introduces a new criterion under standard conjectures to recognize Galois representations arising from K3 surfaces, bridging abstract algebraic and geometric perspectives.

Findings

Provides a criterion assuming major conjectures

Connects Galois representations to K3 surface cohomology

Advances understanding of the relationship between representations and geometry

Abstract

Under the assumption of the Hodge, Tate and Fontaine-Mazur conjectures we give a criterion for a compatible system of l-adic representations to be isomorphic to the second cohomology of a K3 surface.