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 |
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| container_title | Inventiones mathematicae |
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| creator | Friedlander, Eric M. Pevtsova, Julia Suslin, Andrei |
| description | 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. |
| doi_str_mv | 10.1007/s00222-007-0037-2 |
| format | Article |
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| language | eng |
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| subjects | Fields (mathematics) Group theory Studies Subgroups |
| title | Generic and maximal Jordan types |
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