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math.AG2026
Semisimplicity, purity and Mumford-Tate conjecture for hyper-Kähler varieties
Kazuhiro Ito, Haitao Zou
We prove the Mumford-Tate conjecture in every degree for hyper-Kähler varieties over fields finitely generated over . The proof establishes semisimplicity of -adi…
math.NT2026
Close fields, affine Springer fibers and fundamental lemmas
Sebastian Bartling, Kazuhiro Ito
We prove a geometric local constancy theorem for affine Springer fibers in families of close local fields. Consequently, stable orbital integrals are locally constant in these fami…