HPD-invariance of the Tate conjecture

TL;DR

This paper proves that the Tate conjecture remains invariant under Homological Projective Duality, leading to new cases where the conjecture holds, including certain determinantal varieties and orbifolds.

Contribution

It establishes the HPD-invariance of the Tate conjecture and extends its validity to new geometric contexts like stacks and orbifolds.

Findings

Proved Tate conjecture invariance under HPD.

Established Tate conjecture for linear sections of determinantal varieties.

Extended Tate conjecture to certain global orbifolds.

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