Author

Ning Li

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Preprint Sep 2026

The Tate conjecture for powers of abelian fourfolds and the Hodge conjecture for powers of CM fourfolds

We prove the Tate conjecture in every codimension on every power of an abelian variety of dimension at most four over a finite field. For geometrically simple fourfolds, we use Broe's theorem and the classification of Frobenius relations. For dihedral pairs of abelian surfaces, we construct algebraic classes using fami...

Ning Li · 0 citations

Preprint Aug 2026

Exponents of factorized groups and Kashina's conjecture for group-theoretical Hopf algebras

Let $G=F\Gamma$ be a factorization of a finite group, with neither factor assumed normal and with $F\cap\Gamma$ allowed to be nontrivial. We prove that $\exp(G)$ divides $\operatorname{lcm}(|F|,|\Gamma|)$, or equivalently that $\gcd([G:F],[G:\Gamma])\exp(G)$ divides $|G|$. This answers a cohomological divisibility ques...

Ning Li · 0 citations

Preprint Sep 2026

The Tate conjecture for abelian fivefolds over finite fields

We prove the Tate conjecture for abelian fivefolds over finite fields. The proof constructs correspondences for a residual motive using a Moret--Bailly family, Gross--Schoen heights, and monodromy. We also prove standard conjecture~$D_\ell$ over $\overline{\mathbf F}_p$ and independence of $\ell$ of rational cycle clas...

Ning Li · 0 citations