Speaker:	Satoshi Mochizuki (Chuo U)
Title:	Higher derived categories of relative exact categories and non-connective K-theory
Date (JST):	Tue, Nov 12, 2013, 12:00 - 13:00
Place:	Balcony A
Abstract:	For relative exact categories E, we define a family of triangulated categories {D_n(E)} indexed by natural numbers and we call D_n(E) the n-th derived category of E. The 0-th derived category is a usual bounded derived category of E and 1-th derived category is a usual unbounded derived category of E. For relative exact category E, we prove that (1) (-n)-th K-theory of E is a Grothendieck group of idempotent completion of the n-th derived category of E. (2) (-n)-th K-theory of E is trivial if and only if the n-th derived category of E is idempotent complete. Utilizing these tools we give a proof and a strategy for several vanishing conjectures of non-connective K-theory.

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