Generic and maximal Jordan types

For a finite group scheme G over a field k of characteristic p>0, we associate new invariants to a finite dimensional kG-module M. Namely, for each generic point of the projectivized cohomological variety we exhibit a “generic Jordan type” of M. In the very special case in which G=E is an element...

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Veröffentlicht in:Inventiones mathematicae 2007-06, Vol.168 (3), p.485-522
Hauptverfasser: Friedlander, Eric M., Pevtsova, Julia, Suslin, Andrei
Format: Artikel
Sprache:eng
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Zusammenfassung:For a finite group scheme G over a field k of characteristic p>0, we associate new invariants to a finite dimensional kG-module M. Namely, for each generic point of the projectivized cohomological variety we exhibit a “generic Jordan type” of M. In the very special case in which G=E is an elementary abelian p-group, our construction specializes to the non-trivial observation that the Jordan type obtained by restricting M via a generic cyclic shifted subgroup does not depend upon a choice of generators for E. Furthermore, we construct the non-maximal support variety Γ(G)M, a closed subset of which is proper even when the dimension of M is not divisible by p.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-007-0037-2