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K-theory of infinite products

Alexander Efimov
Monday 24 October 2022 15:00 Koll. G (1532-214)
Mathematics Seminar

I will explain a simple proof of the following statement: K-theory of stable infinity-categories commutes with infinite products. This result is due to Kasprowski and Winges (2018), and their proof uses infinity-version of Grayson's construction of binary acyclic complexes to reduce the statement to K_0. A certain non-trivial argument is needed to reduce the length of these binary acyclic complex (namely, length 7 is sufficient).

Our proof instead uses sheaves on the real line instead of the Grayson's construction. The argument reduces to the well-known elementary statement: the derived category of a Dynkin quiver does not depend on the orientation of arrows.

Contact: Sergey Arkhipov Revised: 21.10.2022