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arXiv · 1212.0923

Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II

Jordan S. Ellenberg·Akshay Venkatesh·Craig Westerland
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Abstract

We prove a version of the Cohen--Lenstra conjecture over function fields (completing the results of our prior paper). This is deduced from two more general theorems, one topological, one arithmetic: We compute the direct limit of homology, over puncture-stabilization, of spaces of maps from a punctured manifold to a fixed target; and we compute the Galois action on the set of stable components of Hurwitz schemes.

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Jordan S. Ellenberg, Akshay Venkatesh, Craig Westerland. 2012-12-05. Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II. https://arxiv.org/abs/1212.0923

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