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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