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

@article{Ellenberg2012HomologicalSF,
title={Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II},
author={Jordan S. Ellenberg and Akshay Venkatesh and Craig Westerland},
journal={arXiv: Number Theory},
year={2012}
}
• Published 2 December 2009
• Mathematics
• arXiv: Number Theory
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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