Equivariant isomorphisms of Ext and Tor modules

Abstract

In this article we establish equivariant isomorphisms of Ext and Tor modules over different relative complete intersections. More precisely, for a commutative ring $Q$, this paper investigates how $Ex{t}_{Q/(\mathbf{f})}^{\ast }(M,N)$ and $To{r}_{\ast }^{Q/(\mathbf{f})}(M,N)$ change when one varies $\mathbf{f}$ among all Koszul-regular sequences of a fixed length such that $\mathbf{f}M=0$ and $\mathbf{f}N=0$. Of notable interest is how the theory of perturbations is used to establish isomorphisms of certain DG modules.

13 pages. Comments welcome!