On the integral Tate conjecture for finite fields and representation theory

2015/04/19 by Benjamin Antieau, Antieau, Benjamin
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #math.AG

paper · pdf · doi:10.48550/arxiv.1504.04879

final version, minor typos corrected, 12 pages, to appear in Algebraic Geometry

openalex publication_date 2015/04/19 · arxiv created 2015/05/28 · arxiv updated 2015/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a new source of counterexamples to the so-called integral Hodge and integral Tate conjectures. As in the other known counterexamples to the integral Tate conjecture over finite fields, ours are approximations of the classifying space of some group BG. Unlike the other examples, we find groups of type A_n, our proof relies heavily on representation theory, and Milnor's operations vanish on the classes we construct.

Related

• Further counterexamples to the integral Hodge conjecture
• Note on the counterexamples for the integral Tate conjecture over finite fields
• On the integral Tate conjecture for abelian varieties
• Uniform bounds for obstructions to the integral Tate conjecture
• The Tate conjecture over finite fields (AIM talk)