On the integral Tate conjecture for abelian varieties

2025/09/08 by J. S. Milne, Milne, J. S.
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2509.06707

Abstract

Recently Engel et al. (2025) have shown that the integral Hodge conjecture fails for very general abelian varieties. Using Deligne's theory of absolute Hodge cycles, we deduce a similar statement for the integral Tate conjecture.

Citations

• Matroids and the integral Hodge conjecture for abelian varieties

Related

• The Tate and Standard Conjectures for Certain Abelian Varieties
• A Survey of the Hodge Conjecture for Abelian Varieties
• A survey around the Hodge, Tate and Mumford-Tate conjectures for abelian varieties
• Uniform bounds for obstructions to the integral Tate conjecture
• Integral and Absolute Hodge Classes