### 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.

Language | English |
---|---|

Pages | 485-522 |

Number of pages | 38 |

Journal | Inventiones Mathematicae |

Volume | 168 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2007 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Inventiones Mathematicae*,

*168*(3), 485-522. DOI: 10.1007/s00222-007-0037-2

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

Research output: Research - peer-review › Article

*Inventiones Mathematicae*, vol 168, no. 3, pp. 485-522. DOI: 10.1007/s00222-007-0037-2

}

TY - JOUR

T1 - Generic and maximal Jordan types

AU - Friedlander,Eric M.

AU - Pevtsova,Julia

AU - Suslin,Andrei

PY - 2007/6

Y1 - 2007/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34247489729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247489729&partnerID=8YFLogxK

U2 - 10.1007/s00222-007-0037-2

DO - 10.1007/s00222-007-0037-2

M3 - Article

VL - 168

SP - 485

EP - 522

JO - Inventiones Mathematicae

T2 - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 3

ER -