Ascent properties for derived functors

TL;DR

This paper investigates conditions under which derived functors Tor and Ext for finitely generated modules over a flat local ring homomorphism can be endowed with compatible module structures over the extended ring.

Contribution

It provides new criteria for when Tor and Ext modules inherit compatible S-module structures in the context of flat local ring homomorphisms.

Findings

Identifies conditions for Tor modules to have compatible S-module structures.

Establishes criteria for Ext modules to be S-modules compatible with R-module structures.

Enhances understanding of module structures in flat local ring extensions.

Abstract

Given a flat local ring homomorphism R\to S, and two finitely generated R-modules M and N, we describe conditions under which the modules Tor^i(M,N) and Ext^i(M,N) have S-module structures that are compatible with their R-module structures.