Cohomological Mackey formula for quotient stacks

TL;DR

This paper develops a Mackey-type formula for the critical cohomology of equivariant Landau-Ginzburg models, establishing a new algebraic structure that relates restriction and induction maps in the context of quotient stacks.

Contribution

It introduces a restriction morphism and proves a compatibility formula, providing a novel Mackey-type structure for critical cohomology in algebraic geometry.

Findings

Established a restriction morphism on critical cohomology.

Proved a Mackey-type compatibility formula.

Structured critical cohomology as a localized induction-restriction system.

Abstract

In this paper, we construct a restriction morphism on the critical cohomology of an equivariant Landau-Ginzburg model associated to a representation of a reductive group equipped with an invariant function. We show a compatibility formula between the restriction and induction maps as a Mackey-type formula, thereby giving the critical cohomology the structure of a localized induction-restriction system.