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Algebraic K -theory of the first Morava K -theory

Christian Ausoni, John Rognes (2012)

Journal of the European Mathematical Society

For a prime p 5 , we compute the algebraic K -theory modulo p and v 1 of the mod p Adams summand, using topological cyclic homology. On the way, we evaluate its modulo p and v 1 topological Hochschild homology. Using a localization sequence, we also compute the K -theory modulo p and v 1 of the first Morava K -theory.

On Bott-periodic algebraic K-theory.

Felipe Zaldívar (1994)

Publicacions Matemàtiques

Let K*(A;Z/ln) denote the mod-ln algebraic K-theory of a Z[1/l]-algebra A. Snaith ([14], [15], [16]) has studied Bott-periodic algebraic theory Ki(A;Z/ln)[1/βn], a localized version of K*(A;Z/ln) obtained by inverting a Bott element βn. For l an odd prime, Snaith has given a description of K*(A;Z/ln)[1/βn] using Adams maps between Moore spectra. These constructions are interesting, in particular for their connections with Lichtenbaum-Quillen conjecture [16].In this paper we obtain a description...

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