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.

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

References in corpus (1)

• Affine representability results in ${\mathbb{A}}^1$-homotopy theory I: vector bundles

Cited by in corpus (5)

• K-theory and G-theory of derived algebraic stacks
• Categorical Milnor squares and K-theory of algebraic stacks
• Purity in chromatically localized algebraic $K$-theory
• Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory
• ${\mathbb{A}}^1$-invariance of localizing invariants