On Previdi's delooping conjecture forK-theory

Sho Saito
2015 Algebra & Number Theory  
We prove a modified version of Previdi's conjecture stating that the Waldhausen space (K-theory space) of an exact category is delooped by the Waldhausen space (K-theory space) of Beilinson's category of generalized Tate vector spaces. Our modified version states the delooping with non-connective K-theory spectra, almost including Previdi's original statement. As a consequence we obtain that the negative K-groups of an exact category are given by the 0-th K-groups of the idempotent-completed
more » ... rated Beilinson categories, extending a theorem of Drinfeld on the first negative K-group.
doi:10.2140/ant.2015.9.1 fatcat:6ogqgr3qpbaxlgnnruxbekpdne