## Abstract

Let G be a reductive algebraic group over an algebraically closed field k of characteristic p > 0, and assume p is good for G. Let P be a parabolic subgroup with unipotent radical U. For r ≥ 1, denote by Ga(r) the r-th Frobenius kernel of Ga. We prove that if the nilpotence class of U is less than p, then any embedding of Ga(r) in U lies inside a one-parameter subgroup of U, and there is a canonical way in which to choose such a subgroup. Applying this result, we prove that if p is at least as big as the Coxeter number of G, then the cohomological variety of _{G(r)} is homeomorphic to the variety of r-tuples of commuting elements in N1(g), the [p]-nilpotent cone of Lie(G).

Original language | English |
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Pages (from-to) | 14-26 |

Number of pages | 13 |

Journal | Journal of Algebra |

Volume | 385 |

DOIs | |

State | Published - Jul 1 2013 |

## Keywords

- Algebraic groups
- Support varieties for modules