Back to Commutative Algebra Seminar: Fall 2017
Commutative Algebra Seminar
Date: Thursday, Oct 19, 2017
Time: 2:30PM - 3:20PM
Location: LCB 215
Jonathan Montano
University of Kansas
Title |
Local cohomology of powers of ideals and modules |
Abstract |
Let R be a Noetherian local ring of dimension d. In this work, our first goal is to study the behavior of the sequence of lengths of local cohomology modules of powers of ideals. For homogeneous ideals, we are able to show that after restricting the lower degrees to a linear bound, the sequence does not grow faster than n^d. Combining this result with Kodaira-like vanishing theorems, we obtain that the sequence of lengths grows as expected for several broad classes of ideals. Moreover, we study similar vanishing results for powers of modules. This is joint work with Hailong Dao. |
Commutative Algebra