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Seminar

Fellowship of the Ring, National Seminar: Numbers of Associated Primes of Powers of Ideals May 06, 2021 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: -- MSRI: Online/Virtual
Speaker(s) Irena Swanson (Purdue University)
Description

To attend this seminar, you must register in advance, by clicking HERE.

Video
Abstract/Media

To attend this seminar, you must register in advance, by clicking HERE.

This talk is about associated primes of powers of ideals in Noetherian commutative rings.  By a result of Brodmann, for any ideal $I$ in a ring $R$, the set of associated primes of $I^n$ stabilizes for large $n$.  In general, the number of associated primes can go up or down as $n$ increases.  This talk is about sequences $\{a_n\}$ for which there exists an ideal $I$ in a Noetherian commutative ring $R$ such that the number of associated primes of $R/I^n$ is $a_n$.  A family of examples shows that $I$ may be prime and the number of associated primes of $I^2$ need not be polynomial in the dimension of the ring.

This is a report on four separate projects with Sarah Weinstein, Jesse Kim, Robert Walker, and ongoing work with Roswitha Rissner.

 Notes 1.3 MB application/pdf