Equivariant Elliptic Cohomology and Mapping Stacks

Abstract

We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex numbers and for a quotient stack, this recovers Grojnowski's equivariant elliptic cohomology of the analytification.

56 pages. Published version

References in corpus (7)

• Chiral de Rham complex
• Loop Spaces and Connections
• The elliptic Weyl character formula
• Equivariant Hodge theory and noncommutative geometry
• A Universal HKR Theorem
• Equivariant localization and completion in cyclic homology and derived loop spaces
• Looijenga line bundles in complex analytic elliptic cohomology