$K$-theoretic torsors for infinite dimensional vector bundles of locally compact type

Drinfeld observed that there were apparently two notions of $K$-theory torsor one might expect to associate to a Tate $R$-module, 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.

Keywords

$K$-theoretic torsor, Tate $R$-module

2010 Mathematics Subject Classification

19E99

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This work was supported by the WPI initiative, MEXT, Japan.

Received 15 February 2017

Received revised 26 May 2017

Published 13 December 2017