Unordered resolutions and homological stability for linear groups
K-Theory and Homology
2025-12-23 v1
Abstract
In this paper, we develop a modified proof strategy for homological stability of linear groups, with the general linear groups serving as a primary example. Our arguments are more direct than those in the classical works of Quillen and Suslin--Nesterenko, although they apply only with localized coefficients. The localization at (n-1)! that arises in our approach appears to be closely related to several conjectures of Mirzaii as well as to Suslin's injectivity conjecture.
Cite
@article{arxiv.2512.18110,
title = {Unordered resolutions and homological stability for linear groups},
author = {Ivan Vasilev and Serge Yagunov},
journal= {arXiv preprint arXiv:2512.18110},
year = {2025}
}