2025/11/21 by Fei Hu, Hu, Fei
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2511.17109
We show that the eigenvalues of any polarized endomorphism acting on the ℓ-adic étale cohomology of a smooth projective variety satisfy certain parity and symmetry properties, as predicted by the standard conjectures. These properties were previously known for Frobenius endomorphisms. Besides the hard Lefschetz theorem, a key new ingredient is a recent Weil's Riemann hypothesis-type result due to J.~Xie. We also prove a "Newton over Hodge" type property for abelian varieties and Grassmannians.