HPD-invariance of the Tate conjecture

2017/07/20 by Gonçalo Tabuada, Tabuada, Goncalo
Mathematics · #14A22 #19D35 #19E08 #55N32 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1707.06639

openalex publication_date 2017/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Tate conjecture is invariant under Homological Projective Duality (=HPD). As an application, we prove the Tate conjecture in the new cases of linear sections of determinantal varieties, and also in the cases of complete intersections of two quadrics. Furthermore, we extend the Tate conjecture from schemes to stacks and prove it for certain global orbifolds

Citations

• A remark on hyperplane sections of rational normal scrolls

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