### Abstract

Let G be a reductive algebraic group scheme defined over F-p and G(1) be the first Frobenius kernel. For any dominant weight lambda, one can construct the Weyl module V(lambda). When p is a good prime for G, the G(1)-support variety of V (lambda) was computed by Nakano, Parshall and Vella in [D. K. Nakano, B.J. Parshall, D.C. Vella, Support varieties for algebraic groups, J. Reine Angew. Math. 547 (2002) 15-49]. We complete this calculation by computing the G(1)-supports of the Weyl modules over fields of bad characteristic.

Original language | English |
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Pages (from-to) | 602-633 |

Number of pages | 32 |

Journal | Journal of Algebra |

Volume | 312 |

Issue number | 2 |

Early online date | 21 Mar 2007 |

DOIs | |

Publication status | Published - 15 Jun 2007 |

### Keywords

- cohomology
- support varieties
- Weyl modules
- finite-group schemes
- lie-algebras
- nilpotent elements
- unipotent elements
- field

### Cite this

*Journal of Algebra*,

*312*(2), 602-633. https://doi.org/10.1016/j.jalgebra.2007.03.008