### Abstract

We prove the conjecture of Lusztig in [5, Section 4]. Given a reductive group over F_{q}‾[ε]/(ε^{r}) for some r≥2, there is a notion of a character sheaf defined in [4, Section 8]. On the other hand, there is also a geometric analogue of the character constructed by Gérardin [2]. The conjecture in [5, Section 4] states that the two constructions are equivalent, which Lusztig also proved for r=2,3,4. Here we generalize his method to prove this conjecture for general r. As a corollary we prove that the characters derived from these two complexes are equal.

Original language | English (US) |
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Pages (from-to) | 76-98 |

Number of pages | 23 |

Journal | Journal of Algebra |

Volume | 514 |

DOIs | |

State | Published - Nov 15 2018 |

### Keywords

- Character sheaf

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## Cite this

Kim, D. (2018). A comparison of two complexes.

*Journal of Algebra*,*514*, 76-98. https://doi.org/10.1016/j.jalgebra.2018.07.038