Period sheaves via perverse pullbacks

TL;DR

This paper constructs period sheaves for Hamiltonian spaces using perverse pullback functors, generalizing previous work and connecting to known cases like cotangent and Whittaker spaces.

Contribution

It introduces a new construction of period sheaves via perverse pullbacks, proving a dimensional reduction isomorphism and relating these to microstalk functors.

Findings

Period sheaves recover known constructions in cotangent and Whittaker cases.

Dimensional reduction isomorphism generalizes previous results in cohomological Donaldson--Thomas theory.

Perverse pullbacks refine ordinary pullback functors in constructible sheaf theory.

Abstract

We construct period sheaves for Hamiltonian spaces, as conjectured in the work of Ben-Zvi, Sakellaridis and Venkatesh, using the perverse pullback functors introduced in the authors' previous work. We prove a dimensional reduction isomorphism (generalizing the results of Davison and Kinjo in cohomological Donaldson--Thomas theory) which implies that perverse pullbacks refine the ordinary pullback functors in constructible sheaf theory, and relate perverse pullbacks to microstalk functors. These results imply that our period sheaves recover the known constructions in the cotangent and Whittaker cases.