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Investigating $kG$-modules using nilpotent operators

Presented by: 
E Friedlander [Southern California]
Tuesday 23rd June 2009 - 10:00 to 11:00
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons