44 research outputs found
Hopf algebra structure on topological Hochschild homology
The topological Hochschild homology THH(R) of a commutative S-algebra
(E_infty ring spectrum) R naturally has the structure of a commutative
R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy
category. We show, under a flatness assumption, that this makes the Boekstedt
spectral sequence converging to the mod p homology of THH(R) into a Hopf
algebra spectral sequence. We then apply this additional structure to the study
of some interesting examples, including the commutative S-algebras ku, ko, tmf,
ju and j, and to calculate the homotopy groups of THH(ku) and THH(ko) after
smashing with suitable finite complexes. This is part of a program to make
systematic computations of the algebraic K-theory of S-algebras, by means of
the cyclotomic trace map to topological cyclic homology.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-49.abs.htm
Enriched Reedy categories
We define the notion of an enriched Reedy category and show
that if A is a C-Reedy category for some symmetric monoidal model category
C and M is a C-model category, the category of C-functors and C-natural
transformations from A to M is again a model category.This research was partially conducted during the period the author was employed by the Clay
Mathematics Institute as a Liftoff Fellow
Enriched Reedy categories
We define the notion of an enriched Reedy category, and show that if A is a
C-Reedy category for some symmetric monoidal model category C and M is a
C-model category, the category of C-functors and C-natural transformations from
A to M is again a model category.Comment: The definition of an enriched Reedy category was ever so slightly
imprecise. Version 2 corrects thi
The norm map of Witt vectors
We discuss a multiplicative version of the Verschiebung map of Witt vectors
that we call the norm.Comment: 7 pages. Comments welcom