K. Ito

Semisimplicity, purity and Mumford-Tate conjecture for hyper-K\"ahler varieties

We prove the Mumford-Tate conjecture in every degree for hyper-K\"ahler varieties over fields finitely generated over $\mathbb{Q}$. The proof establishes semisimplicity of $\ell$-adic cohomology by eliminating the unipotent radical of the algebraic monodromy group of total cohomology. We also prove the weight-monodromy...