UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

May 13, 2008

939 Evans Hall


3:45PM: Modules of constant Jordan type

Dave Benson

Let $k$ be an algebraically closed field of characteristic $p$ and let $R$ be the ring $k[x_1,\dots,x_n]/(x_1^p,\dots,x_n^p)$. A f.g. $R$-module is said to have constant Jordan type if the Jordan canonical form of $\lambda_1 x_1 + \dots + \lambda_n x_n$ is independent of $\lambda_1,\dots,\lambda_n$ (provided they're not all zero). This concept was introduced and investigated in a recent paper of Carlson, Friedlander and Pevtsova. I'll describe some examples and some interesting properties of modules of constant Jordan type. I'll explain a theorem I proved a few weeks ago and a conjecture formulated by Rickard even more recently.

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5:00PM: The Homological Conjectures (after Hochster and Roberts)

Simon Schieder

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