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Abstract
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We prove that for a quasiregular semiperfectoid
-algebra
(in
the sense of Bhatt–Morrow–Scholze), the cyclotomic trace map from the
-completed
-theory
spectrum
of
to the topological
cyclic homology
of
identifies
on
with a
-deformation
of the logarithm.
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Keywords
algebraic $K\mkern-2mu$-theory, prisms, cyclotomic trace
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Mathematical Subject Classification 2010
Primary: 19D55, 19F99
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Milestones
Received: 4 November 2019
Revised: 2 April 2020
Accepted: 20 April 2020
Published: 28 July 2020
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