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Talk

January 16, 2024
Christoph Winges (Universität Regensburg): The theorem of the heart fails in nonconnective K-theory

Abstract

Barwick's theorem of the heart asserts that the connective algebraic K-theory of a stable infinity-category with bounded t-structure coincides with that of its heart. I will explain why the analogous statement for nonconnective algebraic K-theory is not true in general. The key ingredients to constructing a counterexample is a version of Auslander's formula for stable infinity-categories and the fact that every spectrum arises as the nonconnective algebraic K-theory of some stable infinity-category. Joint work with Maxime Ramzi and Vladimir Sosnilo.

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