Jon F. Carlson, Eric M. Friedlander, Julia Pevtsova
Published 2007-07-25Version 1
We introduce the class of modules of constant Jordan type for a finite group scheme $G$ over a field $k$ of characteristic $p > 0$. This class is closed under taking direct sums, tensor products, duals, Heller shifts and direct summands, and includes endotrivial modules. It contains all modules in an Auslander-Reiten component which has at least one module in the class. Highly non-trivial examples are constructed using cohomological techniques. We offer conjectures suggesting that there are strong conditions on a partition to be the Jordan type associated to a module of constant Jordan type.
Representations and Cohomology of finite group schemes
Local duality for representations of finite group schemes
The variety of subadditive functions for finite group schemes
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