91 citations · 288 across the 14 of their papers we have counts for
14 papers
Localization sequences for logarithmic topological cyclic homology
John Rognes, Steffen Sagave, Christian Schlichtkrull
We introduce the notion of an E_k-ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context…
Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
Fabian Hebestreit, Steffen Sagave, Christian Schlichtkrull
In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set level framework for parametrized homotopy theory. We provide a convolution smash pr…
Generalized Thom spectra and their topological Hochschild homology
Samik Basu, Steffen Sagave, Christian Schlichtkrull
We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we sh…
Virtual vector bundles and graded Thom spectra
Steffen Sagave, Christian Schlichtkrull
We introduce a convenient framework for constructing and analyzing orthogonal Thom spectra arising from virtual vector bundles. This framework enables us to set up a theory of orie…
Logarithmic topological Hochschild homology of topological K-theory spectra
John Rognes, Steffen Sagave, Christian Schlichtkrull
In this paper we continue our study of logarithmic topological Hochschild homology. We show that the inclusion of the connective Adams summand into the p-local complex connective K…
Braided injections and double loop spaces
Christian Schlichtkrull, Mirjam Solberg
We consider a framework for representing double loop spaces (and more generally E-2 spaces) as commutative monoids. There are analogous commutative rectifications of braided monoid…
Localization sequences for logarithmic topological Hochschild homology
John Rognes, Steffen Sagave, Christian Schlichtkrull
We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for ex…
Group completion and units in I-spaces
Steffen Sagave, Christian Schlichtkrull
The category of I-spaces is the diagram category of spaces indexed by finite sets and injections. This is a symmetric monoidal category whose commutative monoids model all E-infini…
Diagram spaces and symmetric spectra
Steffen Sagave, Christian Schlichtkrull
We present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra. The main motivating examples are the I-spaces, which are diagr…
The cyclotomic trace for symmetric ring spectra
Christian Schlichtkrull
The purpose of this paper is to present a simple and explicit construction of the Bokstedt-Hsiang-Madsen cyclotomic trace relating algebraic K-theory and topological cyclic homolog…
Topological Hochschild homology of Thom spectra and the free loop space
A. J. Blumberg, R. L. Cohen, C. Schlichtkrull
We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibra…
Higher topological Hochschild homology of Thom spectra
Christian Schlichtkrull
In this paper we analyze the higher topological Hochschild homology of commutative Thom S-algebras. This includes the case of the classical cobordism spectra MO, MSO, MU, etc. We c…
Thom spectra that are symmetric spectra
Christian Schlichtkrull
We analyze the functorial and multiplicative properties of the Thom spectrum functor in the setting of symmetric spectra, and we establish the relevant homotopy invariance.
Units of ring spectra and their traces in algebraic K-theory
Christian Schlichtkrull
Let GL_1(R) be the units of a commutative ring spectrum R. In this paper we identify the composition BGL_1(R)->K(R)->THH(R)->Ω^{\infty}(R), where K(R) is the algebraic K-theory and…