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Uniform twisted homological stability

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arxiv 2402.00354 v4 pith:UZOKX54J submitted 2024-02-01 math.AT math.NT

Jeremy Miller , Peter Patzt , Dan Petersen , Oscar Randal-Williams This is my paper · ORCID
classification math.ATmath.NT
keywords groupshomologicalstabilityalgebraicarithmeticautomorphismbergstrbraid
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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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Cited by 1 Pith paper

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  1. Representation stability for ordered Hurwitz spaces

    math.AT 2025-09 conditional novelty 7.0 of 10

    The homology groups of ordered Hurwitz spaces, seen as representations of symmetric groups, have stable multiplicities in a range that grows linearly with homological degree.

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