2017/03/31 by Georg Tamme · 1 citation
Mathematics · #math.KT #math.RA
paper · pdf · doi:10.1112/s0010437x18007236
published as Compositio Math. 154 (2018) 1801-1814 · 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
arxiv created 2018/05/28 · arxiv updated 2019/02/20
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.