Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II
arXiv:1212.0923
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.
This article has been temporarily withdrawn owing to a gap which affects Section 6, 12 and some theorems of the introduction: the homological stabilization maps used in this paper and the previous paper are not exactly the same. We have been able to fix this under additional restrictions, although not in general. A modified version will be posted in the next few weeks
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