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Presented By: Department of Mathematics

Student Commutative Algebra Seminar

Symbolic Powers and the containment problem

We will discuss some basic properties of symbolic powers of a prime ideal. In particular, we will see why the n-th symbolic power of a prime ideal P captures the notion of functions that vanish to order at least n on the subvariety defined by P in a polynomial ring of char 0. After that, we will prove that if P is a prime ideal of height c in a regular domain R of char p > 0, then the (cn)-th symbolic power is contained in the n-th ordinary power of P. Speaker(s): Karthik Ganapathy (University of Michigan Ann Arbor)

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