Excision in algebraic K-theory revisited
Abstract
By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic K-theory. We give a new and direct proof of Suslin's result based on an exact sequence of categories of perfect modules. In fact, we prove a more general descent result for a pullback square of ring spectra and any localizing invariant. Besides Suslin's result, this also contains Nisnevich descent of algebraic K-theory for affine schemes as a special case. Moreover, the role of the Tor-unitality condition becomes very transparent.
Cite
@article{arxiv.1703.03331,
title = {Excision in algebraic K-theory revisited},
author = {Georg Tamme},
journal= {arXiv preprint arXiv:1703.03331},
year = {2019}
}
Comments
v2: improved exposition v3: major revision: removed unnecessary connectivity assumption, formulated a general criterion saying when a diagram of small stable $\infty$-categories yields a pullback diagram after applying a localizing invariant