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Algebraic K-theory of the first Morava K-theory Christian Ausoni John Rognes
 

Summary: Algebraic K-theory of the first Morava K-theory
Christian Ausoni John Rognes
8. February 2011
Abstract
For a prime p 5, we compute the algebraic K-theory modulo p and v1 of
the mod p Adams summand, using topological cyclic homology. On the way, we
evaluate its modulo p and v1 topological Hochschild homology. Using a localization
sequence, we also compute the K-theory modulo p and v1 of the first Morava K-
theory.
Keywords. Algebraic K-theory, Morava K-theory, topological cyclic homology, to-
pological Hochschild homology
1 Introduction
In this paper we continue the investigation from [AR02] and [Aus10] of the algebraic K-
theory of topological K-theory and related S-algebras. Let p be the p-complete Adams
summand of connective complex K-theory, and let /p = k(1) be the first connective
Morava K-theory. It has a unique S-algebra structure [Ang, Th. A], and we show in
Section 2 that /p is an p-algebra (in uncountably many ways), so that K( /p) is a K( p)-
module spectrum.
Let V (1) = S/(p, v1) be the type 2 Smith­Toda complex (see Section 4 below for
a definition). It is a homotopy commutative ring spectrum for p 5, with a preferred

  

Source: Ausoni, Christian - Institut für Mathematische Statistik, Westfälische Wilhelms Universität Münster

 

Collections: Mathematics