On Previdi's delooping conjecture for K-theory

Abstract

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 iterated Beilinson categories, extending a theorem of Drinfeld on the first negative K-group.

9 pages

Cited by in corpus (4)

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• Reciprocity laws and $K$-theory
• The Index Map in Algebraic K-Theory
• Hochschild coniveau spectral sequence and the Beilinson residue