HPD-invariance of the Tate, Beilinson and Parshin conjectures

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.

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

References in corpus (3)

• Semiorthogonal decompositions in algebraic geometry
• A remark on hyperplane sections of rational normal scrolls
• On Grothendieck's standard conjectures of type C and D in positive characteristic

Cited by in corpus (1)

• Cycle maps on cohomology theories for dg-categories and their applications