Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
GUIDO'S BOOK OF CONJECTURES 1 1. THE CHROMATIC RED-SHIFT IN ALGEBRAIC K -THEORY
 

Summary: GUIDO'S BOOK OF CONJECTURES 1
1. THE CHROMATIC RED-SHIFT IN ALGEBRAIC K -THEORY
Christian Ausoni and John Rognes
The algebraic K -theory of the sphere spectrum S is of interest in geometric
topology, by Waldhausen's stable parametrized h-cobordism theorem [WJR]
(ca. 1979). We wish to understand KS like we understand KZ, via Galois
descent. As a building block, the algebraic K -theory of the Bousfield
localization LK(n)S of S with respect to the n-th Morava K-theory K(n)
might be more accessible. John has developed a theory of Galois extensions for
S-algebras, and in this framework he has stated extensions of the Lichtenbaum-
Quillen conjectures. Their precise formulation is distilled from the clues
provided by our computations of the algebraic K -theory of topological K -
theory and related spectra, and it is to be expected that they will keep maturing
in a cask of skepticism for a few years. Writing XhG
for the homotopy fixed-
point spectrum of a finite group G acting on a spectrum X, we recall:
DEFINITION 1.1 ([Ro]). A map A B of commutative S-algebras is
a K(n)-local G-Galois extension if G acts on B through commutative A-
algebra maps, and the canonical maps A BhG
and B A B G B are

  

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

 

Collections: Mathematics