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math.AG2026
On the Hodge conjecture for hyper-Kähler varieties of generalized Kummer type of dimension divisible by four
Salvatore Floccari, Lie Fu
We prove the Hodge conjecture for all hyper-Kähler varieties of generalized Kummer type of dimension with a prime number, and all powers of these varieties. For any vari…
math.AG2026
Supersingular Tate conjecture for irreducible symplectic varieties of known types: I
Lie Fu, Xuanlin Huang, Zhiyuan Li
We prove that for a supersingular irreducible symplectic variety admitting suitable lifting to characteristic zero has Tate Chow motive if it is of deformation type , OG6…
math.AG2026
The hyper-Kummer construction
Salvatore Floccari, Lie Fu
The hyper-Kummer construction, discovered by the first-named author, associates a hyper-Kähler manifold of -type with any hyper-Kähler sixfold of generalized Kum…