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Investigating $kG$-modules using nilpotent operators

Friedlander, E (Southern California)
Tuesday 23 June 2009, 10:00-11:00

Seminar Room 1, Newton Institute


This is a report of on-going work with Jon Carlson, Julia Pevtsova, and Andrei Suslin. Our object of study is the representation theory of $kG$ where $G$ is a finite group scheme. Following Quillen's early work, first invariants involve cohomology and cohomological support varieties. These have interpretations in terms of 1-parameter subgroups and $\pi$-points. Finer invariants arise from considering the Jordan type of nilpotent operators, leading to local Jordan types, generalized support varieties, and algebraic vector bundles on projective varieties.


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