UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 08, 2016

939 Evans Hall

3:45PM: Symbolic powers and the question of uniform growth

Craig Huneke

Symbolic powers of prime ideals are a basic construction in commutative algebra, in many ways nicer and more geometric than the ordinary powers. There are many open problems about them, some of which center on comparing them to ordinary powers. This talk will give background on these questions, and then focus on the following: let (R,m) be a complete local domain. Does there exist an integer k such that for all prime ideals P in R and all n > 0, the (kn)^{th} symbolic power of P is in the n^{th} power of P? In developing work with Daniel Katz, we can give a positive answer for abelian extensions of regular local rings. I will focus on the easiest case of adjoining a square root to illustrate the issues.

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