Regularity of Tor for weakly stable ideals

TL;DR

This paper proves that the regularity of certain Tor modules involving weakly stable ideals in polynomial rings has the expected upper bounds, and provides bounds for Ext modules as well.

Contribution

It establishes new bounds on the regularity of Tor and Ext modules for weakly stable ideals, extending understanding of their homological properties.

Findings

Regularity of Tor modules has the expected upper bound for weakly stable ideals.

Provides bounds for the regularity of Ext modules involving weakly stable ideals.

Enhances understanding of homological invariants of weakly stable ideals.

Abstract

It is proved that if $I$ and $J$ are weakly stable ideals in a polynomial ring $R=k[x_1,\ldots,x_n]$, with $k$ a field, then the regularity of $\text{Tor}^R_i(R/I,R/J)$ has the expected upper bound. We also give a bound for the regularity of $\text{Ext}_R^i(R/I,R)$ for $I$ a weakly stable ideal.