Adelic Descent for Equivariant Elliptic Cohomology

Abstract

We define $k$-rationalized $G$-equivariant elliptic cohomology, for a field of characteristic zero $k$ and a compact Lie group $G$, via adelic descent. We also give adelic descriptions of rationalized $G$-equivariant singular cohomology and K-theory. This completes a program first proposed by Roşu. These descriptions are then used to obtain comparison results with periodic cyclic homology theories defined via derived algebraic geometry.

28 pages. Corrected mistakes in Section 5.2. Minor revisions throughout