## 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.

 Attachments 2008-05-13benson.pdf, courtesy of Bjorn Poonen Note: If you right click on the link to "Save file as..." and the filename shows ShowFile.htm, please rename this to the filename that you clicked on.

## Simon Schieder

 Attachments 2008-05-13schieder.pdf, courtesy of Bjorn Poonen Note: If you right click on the link to "Save file as..." and the filename shows ShowFile.htm, please rename this to the filename that you clicked on.