Uniform twisted homological stability
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910981009965056 |
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| author | Miller, Jeremy Patzt, Peter Petersen, Dan Randal-Williams, Oscar |
| author_facet | Miller, Jeremy Patzt, Peter Petersen, Dan Randal-Williams, Oscar |
| contents | We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic groups. The novelty is that the stable range is independent of the choice of representation. Combined with earlier work of Bergström--Diaconu--Petersen--Westerland this proves the Conrey--Farmer--Keating--Rubinstein--Snaith predictions for all moments of the family of quadratic $L$-functions over function fields, for sufficiently large odd prime powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform twisted homological stability Miller, Jeremy Patzt, Peter Petersen, Dan Randal-Williams, Oscar Algebraic Topology Number Theory 55P48, 55U10, 20F36, 11R59 We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic groups. The novelty is that the stable range is independent of the choice of representation. Combined with earlier work of Bergström--Diaconu--Petersen--Westerland this proves the Conrey--Farmer--Keating--Rubinstein--Snaith predictions for all moments of the family of quadratic $L$-functions over function fields, for sufficiently large odd prime powers. |
| title | Uniform twisted homological stability |
| topic | Algebraic Topology Number Theory 55P48, 55U10, 20F36, 11R59 |
| url | https://arxiv.org/abs/2402.00354 |