Character Sheaves on Reductive Lie Algebras in Positive Characteristic

Abstract

We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and only if it has nilpotent singular support and is quasi-admissible. We also present geometric proofs, in positive characteristic, of the equivalence between being admissible and being a character sheaf, and various characterisations of cuspidal sheaves, following the work of Mirković.

14 pages, v2: see the footnote to Theorem 4.1.4

References in corpus (2)

• Character sheaves in characteristic $p$ have nilpotent singular support
• The Fourier Transform and Characteristic Cycles of Monodromic $\ell$-adic Sheaves