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Commutative Algebra Seminar

A counterexample to the existence of Ulrich modules
Thursday, October 10, 2019
3:00-4:00 PM
4088 East Hall Map
Ulrich modules were introduced by Bernd Ulrich in 1984 and has since been a very active area of research. The existence of Ulrich modules over local rings have powerful applications. For example, existence implies Lech's conjecture: given a flat local map of local rings from R to S, the Hilbert-Samuel multiplicity of S is at least the Hilbert-Samuel multiplicity of R. Until recently, it was unknown if there were any counterexamples to the existence of Ulrich modules. In this talk, I will introduce the notion of Ulrich modules and survey what is known about existence. Then I will give a counterexample to the existence of Ulrich modules. Time permitting, I will also give the first (to the best of my knowledge) counterexample to localization, i.e. Ulrich modules do not always localize. Speaker(s): Farrah Yhee (University of Michigan)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics