Character Sheaves on Reductive Lie Algebras in Positive Characteristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909199773990912 |
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| author | Zhou, Tong |
| author_facet | Zhou, Tong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Character Sheaves on Reductive Lie Algebras in Positive Characteristic Zhou, Tong Representation Theory Algebraic Geometry 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. |
| title | Character Sheaves on Reductive Lie Algebras in Positive Characteristic |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2404.19210 |