K-theoretic obstructions to bounded t-structures
Algebraic K-theory is a powerful invariant of rings, schemes, and their derived analogues. The negative K-groups are of a somewhat different nature than the positive K-groups and are related to the existence of singularities. In this talk, we will recall the definition of stable infinity categories (the higher categorical analogue of triangulated categories) and their algebraic K-theory, and show that the negative K-groups of a stable infinity category vanish whenever the stable infinity category supports a bounded t-structure with noetherian heart. Time permitting, we will discuss a number of applications. This is joint work with B. Antieau and J. Heller.
Dr David Gepner, University of Melbourne