Let A be a commutative ring and let B be a commutative A-algebra. Let d be a positive integer, and let M be an A-module satisfying $\operatorname{Tor}_A^n(B,M)=0 ~~$for $~0\lt n\le d~.$ Prove that for any B-module N there exists an isomorphism $\operatorname{Ext}_B^m(B\otimes_A M,N)\cong \operatorname{Ext}_A^m(M,N)$ for every $m\leq d$
Asked
Active
Viewed 64 times
2
-
1Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Jul 23 '19 at 07:51