The integral Hodge conjecture for two-dimensional Calabi–Yau categories

Compositio mathematica

article

Alexander Perry¹ 

[1] Department of Mathematics, University of Michigan

关键词: noncommutative variety;    integral Hodge conjecture;    Calabi–Yau category;    K3 surface;    intermediate Jacobian;    14F08;    14A22;    14C30;    14J28;    14J45;   

DOI  :  10.1112/S0010437X22007266

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi–Yau categories which are suitably deformation equivalent to the derived category of a K3 or abelian surface, and use this to deduce cases of the usual integral Hodge conjecture for varieties. Along the way, we prove a version of the variational integral Hodge conjecture for families of two-dimensional Calabi–Yau categories, as well as a general smoothness result for relative moduli spaces of objects in such families. Our machinery also has applications to the structure of intermediate Jacobians, such as a criterion in terms of derived categories for when they split as a sum of Jacobians of curves.

【 授权许可】

CC BY