Generic and maximal Jordan types

Eric M. Friedlander, Julia Pevtsova, Andrei Suslin

Research output: Contribution to journalArticle

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Abstract

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 Proj Ḣ(G,k)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 Proj Ḣ (G,k) which is proper even when the dimension of M is not divisible by p.

LanguageEnglish (US)
Pages485-522
Number of pages38
JournalInventiones Mathematicae
Volume168
Issue number3
DOIs
StatePublished - Jun 1 2007

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Group Scheme
P-groups
Divisible
Finite Group
Subgroup
Generator
Closed
Module
Subset
Invariant
Observation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Friedlander, E. M., Pevtsova, J., & Suslin, A. (2007). Generic and maximal Jordan types. Inventiones Mathematicae, 168(3), 485-522. DOI: 10.1007/s00222-007-0037-2
Friedlander, Eric M. ; Pevtsova, Julia ; Suslin, Andrei. / Generic and maximal Jordan types. In: Inventiones Mathematicae. 2007 ; Vol. 168, No. 3. pp. 485-522
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Friedlander, EM, Pevtsova, J & Suslin, A 2007, 'Generic and maximal Jordan types' Inventiones Mathematicae, vol 168, no. 3, pp. 485-522. DOI: 10.1007/s00222-007-0037-2

Generic and maximal Jordan types. / Friedlander, Eric M.; Pevtsova, Julia; Suslin, Andrei.

In: Inventiones Mathematicae, Vol. 168, No. 3, 01.06.2007, p. 485-522.

Research output: Contribution to journalArticle

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Friedlander EM, Pevtsova J, Suslin A. Generic and maximal Jordan types. Inventiones Mathematicae. 2007 Jun 1;168(3):485-522. Available from, DOI: 10.1007/s00222-007-0037-2