Geometry Seminar

Date: December 5, 2016

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Roberto Barrera, TAMU

Title: A finiteness result for local cohomology modules of Stanley-Reisner rings

Abstract: While local cohomology modules of a ring may not be finitely generated, they still may possess other finiteness properties. In 1990, Craig Huneke asked if the number of associated prime ideals of a local cohomology module is finite. Huneke's question has since been answered in the affirmative for various families of rings by using different methods in characteristic 0 and in positive characteristic. In 2010, Gennady Lyubeznik gave a characteristic free proof that the local cohomology modules of the polynomial ring have finitely many associated prime ideals. In this talk, I will give the necessary background from D-module theory and local cohomology and then answer Huneke's question for local cohomology modules of Stanley-Reisner rings using techniques inspired by Lyubeznik. This is joint work with Jeffrey Madsen and Ashley Wheeler.