戴德金域上一般线性群的同调稳定性

arXiv - MATH - K-Theory and Homology Pub Date : 2024-05-13 DOI:arxiv-2405.07566

Oscar Randal-Williams

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引用次数: 0

摘要

我们证明了在戴德金域上有限生成的投影模的自变群的一种新的同调稳定性定理，它考虑到了这些自变群之间所有可能的稳定映射，而不仅仅是秩1的自由模的稳定映射。我们为克劳森和扬森的还原性玻雷--塞雷空间证明了同样的稳定条件。

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Homological stability for general linear groups over Dedekind domains

We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible stabilisation maps between these, rather than only stabilisation by the free module of rank 1. We show the same kind of stability holds for Clausen and Jansen's reductive Borel--Serre spaces.

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arXiv - MATH - K-Theory and Homology

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