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arXiv · 2402.00354

Uniform twisted homological stability

Jeremy Miller·Peter Patzt·Dan Petersen·Oscar Randal-Williams
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Abstract

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 Bergstr\"om--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.

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Jeremy Miller, Peter Patzt, Dan Petersen, Oscar Randal-Williams. 2024-02-01. Uniform twisted homological stability. https://arxiv.org/abs/2402.00354

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