We prove a modified version of Previdi's conjecture stating that the Waldhausen space (Ktheory 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.
Highly purified beta-core fragment was obtained from urine of a pregnant woman with use of an immunoaffinity column. The amino acid sequence of beta-core fragment indicated that it is composed of two polypeptides linked by a disulfide bond. The two polypeptides correspond to the 6-40 and 55-92 portions of hCG beta-subunit. Both Asn13 and Asn30 residues were glycosylated. The N-linked sugar chains of beta-core fragment were quantitatively released as radioactive oligosaccharides by hydrazinolysis, followed by N-acetylation and NaB3H4 reduction. The radioactive oligosaccharides were fractionated by serial lectin column chromatography and Bio-Gel P-4 column chromatography, and their structures were investigated by sequential exoglycosidase digestion and periodate oxidation. The results indicated that they were a mixture of the four oligosaccharides: Man alpha 1----6(+/- Man alpha 1----3)Man beta 1----4GlcNAc beta 1----4(+/- Fuc alpha 1----6)GlcNAc. The structural characteristics of the sugar chains of beta-core fragment are quite different from those of the beta-subunit of hCG whose structures were typical biantennary sugar chains containing the Neu5Ac alpha 2----3Gal beta 1----4GlcNAc beta 1----2 group as their outer chains.
Drinfeld observed that there were apparently two notions of K-theory torsor one might expect to associate to a Tate Rmodule, and that these should be equivalent. The purpose of the present note is to explain this equivalence as a direct consequence of the author's delooping theorem and Drinfeld's theorem that the first negative K-group vanishes Nisnevich locally.
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