### 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 |
---|---|

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

**Support varieties for Weyl modules over bad primes.** / Benson, David John; Boe, Brian D.; Chastkofsky, Leonard; Nakano, Daniel K.; Jang Hyun, Jo; Kujawa, Jonathan; Mazza, Nadia; Bergonio, Philip; Cooper, Bobbe; Hower, Jeremiah; Platt, Kenyon J.; Wright, Caroline; UGA VIGRE Algebra Group.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 312, no. 2, pp. 602-633. https://doi.org/10.1016/j.jalgebra.2007.03.008

}

TY - JOUR

T1 - Support varieties for Weyl modules over bad primes

AU - Benson, David John

AU - Boe, Brian D.

AU - Chastkofsky, Leonard

AU - Nakano, Daniel K.

AU - Jang Hyun, Jo

AU - Kujawa, Jonathan

AU - Mazza, Nadia

AU - Bergonio, Philip

AU - Cooper, Bobbe

AU - Hower, Jeremiah

AU - Platt, Kenyon J.

AU - Wright, Caroline

AU - UGA VIGRE Algebra Group

PY - 2007/6/15

Y1 - 2007/6/15

N2 - 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.

AB - 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.

KW - cohomology

KW - support varieties

KW - Weyl modules

KW - finite-group schemes

KW - lie-algebras

KW - nilpotent elements

KW - unipotent elements

KW - field

U2 - 10.1016/j.jalgebra.2007.03.008

DO - 10.1016/j.jalgebra.2007.03.008

M3 - Article

VL - 312

SP - 602

EP - 633

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -