The Mumford–Tate conjecture for the product of an abelian surface and a K3 surface

J.M. Commelin

Input for the conjecture

\(\mathrm{H}^{i}_{\textrm{B}}(X)\) — Hodge theory

\(\mathrm{H}^{i}_{\ell}(X)\) — Étale cohomology

Mumford–Tate conjecture

Known cases of the Mumford–Tate conjecture

Main theorem

Remarks about the theorem

More remarks

Hodge theory of K3 surfaces

Proof strategy

Proof: part 1

Proof: part 2

Proof: part 3