Betti Tate's thesis and the trace of perverse schobers

TL;DR

This paper proposes a conjecture on the categorical trace of perverse schobers, linking geometric and mirror symmetry concepts, and proves it in a specific case through Betti Tate's thesis and existing results.

Contribution

It introduces a new conjecture on the categorical trace of perverse schobers and proves it in a key case by combining Betti Tate's thesis with mirror symmetry and spectral trace results.

Findings

Established the conjecture in the simplest case

Connected Betti Tate's thesis with categorical traces

Linked geometric and mirror symmetry frameworks

Abstract

We propose a conjecture on the categorical trace of the 2-category of perverse schobers (expected to model the Fukaya-Fueter 2-category of a holomorphic symplectic space). By proving a Betti geometric version of Tate's thesis, and combining it with our previous 3d mirror symmetry equivalence and the Ben-Zvi--Nadler--Preygel result on spectral traces, we are able to establish our conjecture in the simplest interesting case.