HPD-invariance of the Tate, Beilinson and Parshin conjectures
Algebraic Geometry
2018-05-07 v3 Algebraic Topology
K-Theory and Homology
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1712.05397,
title = {HPD-invariance of the Tate, Beilinson and Parshin conjectures},
author = {Goncalo Tabuada},
journal= {arXiv preprint arXiv:1712.05397},
year = {2018}
}
Comments
21 pages. Revised version: making use of topological periodic cyclic homology, I added similar results concerning the p-version of the Tate conjecture. arXiv admin note: text overlap with arXiv:1707.06639