Year: 2026
Type: preprint
Abstract: We prove the Mumford-Tate conjecture in every degree for hyper-Kähler 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 conjecture for hyper-Kähler varieties over $p$-adic fields. For hyper-Kähler varieties over number fields with $b_2\geq 4$, we establish, after suitable finite extensions, strong compatibility of the associated Weil-Deligne representations valued in Mumford-Tate groups and its integral refinement away from finitely many primes.
Source: arXiv (Cornell University)
Authors: Ito, Kazuhiro, Zou, Haitao
Institutions: Bielefeld University, Tohoku University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221023120