### Abstract

Let

*G*be the group of rational points of a connected reductive group defined over a finite field of characteristic*p*, and let*O*be any commutative ring in which*p*is invertible. We prove that the duality operation of Alvis, Curtis, Kawanka and Lusztig on the characters of*G*is induced by a self-equivalence of the derived category of*OG*-modules, which was conjectured by Broue. We also prove that this equivalence of derived categories is compatible with Harish-Chandra induction and truncation.Translated title of the contribution | Alvis-Curtis duality as an equivalence of derived categories |
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Original language | English |

Title of host publication | Modular Representation Theory of Finite Groups |

Editors | Michael J Collins, Brian Parshall, Leonard L Scott |

Publisher | de Gruyter |

Pages | 157 - 174 |

Number of pages | 18 |

ISBN (Print) | 3110163675 |

Publication status | Published - 2001 |

### Bibliographical note

Other identifier: 9783110163674## Fingerprint Dive into the research topics of 'Alvis-Curtis duality as an equivalence of derived categories'. Together they form a unique fingerprint.

## Cite this

Cabanes, M., & Rickard, JC. (2001). Alvis-Curtis duality as an equivalence of derived categories. In M. J. Collins, B. Parshall, & L. L. Scott (Eds.),

*Modular Representation Theory of Finite Groups*(pp. 157 - 174). de Gruyter.