Home /  Workshop /  Schedules /  Lengths Of Local Cohomology Using Some Surprising Hilbert Kunz Functions

Lengths Of Local Cohomology Using Some Surprising Hilbert Kunz Functions

Connections Workshop: Commutative Algebra January 18, 2024 - January 19, 2024

January 18, 2024 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Jennifer Kenkel (Grinnell College)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Lengths Of Local Cohomology Using Some Surprising Hilbert Kunz Functions

Abstract

We investigate the lengths of certain local cohomology modules over polynomial rings. By fixing the degree component, and using the fact that the length of an Artinian ring is the same as that of its injective hull, we transform this into a question about rings of the form $k[x_1,\dots,x_n]/(x_1^{d_1}, \dots, x_n^{d_n})$ and the annihilator of $x_1 + \dots + x_n$ therein. We in particular use refinements of functions introduced by Han and Monsky. This was motivated by questions about behavior of the length of local cohomology with support in the maximal ideal of thickenings, that is, $R/I^t$ as $t$ grows. This project is joint work with Mel Hochster.

Supplements No Notes/Supplements Uploaded
Video/Audio Files

Lengths Of Local Cohomology Using Some Surprising Hilbert Kunz Functions

Troubles with video?

Please report video problems to itsupport@slmath.org.

See more of our Streaming videos on our main VMath Videos page.