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

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

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