Homological subsets of Spec

Abstract

We recover some data of a module $M$ from the Ext-family $\{Ex{t}_R^i(M,R)\}$. In this regard, we investigate homological subsets of $Spec(R)$, defined by the help of Ext-family. For example, we present a situation for which ${\bigcup }_{i=0}^{\infty }Ass(Ex{t}_R^i(M,R))$ is infinite, thereby answering a question of Vasconcelos. We extend Grothendieck's calculation of $dim(Ex{t}_R^g(M,R))$ and present some new situations to calculate $dim(Ex{t}_R^{\ast }(M,R))$. Also, we compute support and the set of all associated prime ideals of the Ext-family in a serial of nontrivial cases.

arXiv commentDedicated to the memory of Wolmer V. Vasconcelos

Cited by in corpus (1)

• Cohomological splitting, realization, and finiteness