Vladimir Sosnilo | Excision for K-theory with respect to categorical Milnor squares 1/2 (in Russian)
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 06/11/2020

Seminar on A1-topology, motives and K-theory, September 24, 2020
Vladimir Sosnilo (PDMI RAS, SPbU)
Excision for algebraic K-theory with respect to categorical Milnor squares (1/2) (in Russian)


In this talk we will define a Milnor square of stable infinity-categories. We will prove that the nonconnective K-theory sends such a square to a homotopy pullback square of spectra. In particular, there is associated long exact sequence of K-groups. We will explain the relation between the new notion and Milnor squares of rings. The classical Milnor excision result of Suslin and Wodzicki will follow from this result. More generally, the theorem generalizes a recent result of Land and Tamme about the K-theory of pullbacks of A-infinity rings.