A counterexample to the theorem of the heart
Organizers
Speaker
Vladimir Sosnilo
Time
Thursday, September 5, 2024 2:30 PM - 4:00 PM
Venue
A3-2a-302
Online
Zoom 482 240 1589
(BIMSA)
Abstract
Bounded t-structures on triangulated categories are an important tool in homological algebra and complex geometry, that allows one to work with the category as it is the bounded derived category of ab abelian category called the heart. K-theory of triangulated categories is an invariant that recovers algebraic K-theory of rings and schemes. It has been observed by Antieau, Gepner, and Heller that if C admits a bounded t-structure then K_n(C) = K_n(D^b(A)), at least when the heart A is a noetherian abelian category. They conjectured that it's true in general. We construct a counterexample to this conjecture.