Formality of derived intersections and the orbifold HKR isomorphism

TL;DR

This paper investigates the conditions under which derived intersections are formal, leading to new results in derived base change, fixed loci of group actions, and orbifold Hochschild (co)homology decompositions.

Contribution

It introduces criteria for formality of derived intersections and applies these to derive new proofs of the orbifold HKR isomorphism and related structures.

Findings

Derived intersection formality criteria established

Derived base change theorem for non-transversal intersections

New proofs of orbifold Hochschild (co)homology decompositions

Abstract

We study when the derived intersection of two smooth subvarieties of a smooth variety is formal. As a consequence we obtain a derived base change theorem for non-transversal intersections. We also obtain applications to the study of the derived fixed locus of a finite group action and argue that for a global quotient orbifold the exponential map is an isomorphism between the Lie algebra of the free loop space and the loop space itself. This allows us to give new proofs of the HKR decomposition of orbifold Hochschild (co)homology into twisted sectors.