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

Uniform twisted homological stability

Jeremy Miller , Peter Patzt , Dan Petersen , Oscar Randal-Williams This is my paper

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classification math.AT math.NT
keywords groupshomologicalstabilityalgebraicarithmeticautomorphismbergstrbraid
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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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