A counterexample to the nonconnective theorem of the heart
Let C be a stable infinity-category equipped with a bounded t-structure with the heart denoted by A. Antieau, Gepner, and Heller conjectured that the map of nonconnective K-theory spectra K(A) ----> K(C) is always an equivalence. Barwick's theorem of the heart implies that this map is an equivalence on connective covers, and both sides are known to be connective if A is a noetherian abelian category.
To any spectrum M we functorially assign a stable infinity-category C_M such that the spectrum K(C_M) is equivalent to M.
Using this result and some basic chromatic homotopy theory, we construct a counterexample to the conjecture above.
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Organizer
- Victor Roca Lucio
Contact
- Maroussia Schaffner