A comparison of two complexes

Dongkwan Kim

Research output: Contribution to journalArticlepeer-review


We prove the conjecture of Lusztig in [5, Section 4]. Given a reductive group over Fq‾[ε]/(εr) 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 languageEnglish (US)
Pages (from-to)76-98
Number of pages23
JournalJournal of Algebra
StatePublished - Nov 15 2018

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© 2018 Elsevier Inc.


  • Character sheaf


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