2017/12/14 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.1712.05397
openalex publication_date 2017/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the Tate, Beilinson and Parshin conjectures are invariant under Homological Projective Duality (=HPD). As an application, we obtain a proof of these celebrated conjectures (as well as of the strong form of the Tate conjecture) in the new cases of linear sections of determinantal varieties and complete intersections of quadrics. Furthermore, we extend the original conjectures of Tate, Beilinson and Parshin from schemes to stacks and prove these extended conjectures for certain low-dimensional global orbifolds.