46 citations · 350 across the 36 of their papers we have counts for
6 papers · 1 filter
On localization sequences in the algebraic K-theory of ring spectra
Benjamin Antieau, Tobias Barthel, David Gepner
We identify the -theoretic fiber of a localization of ring spectra in terms of the -theory of the endomorphism algebra spectrum of a Koszul-type complex. Using this identific…
Chromatic completion
Tobias Barthel
We study the limit of the chromatic tower for not necessarily finite spectra, obtaining a generalization of the chromatic convergence theorem of Hopkins and Ravenel. Moreover, we p…
A simple universal property of Thom ring spectra
Omar Antolín-Camarena, Tobias Barthel
We give a simple universal property of the multiplicative structure on the Thom spectrum of an -fold loop map, obtained as a special case of a characterization of the algebra st…
Chromatic fracture cubes
Omar Antolín-Camarena, Tobias Barthel
In this note, we construct a general form of the chromatic fracture cube, using a convenient characterization of the total homotopy fiber, and deduce a decomposition of the E(n)-lo…
The -term of the -local -Adams spectral sequence
Tobias Barthel, Drew Heard
Let be Morava -theory of height . In previous work Devinatz and Hopkins introduced the -local -Adams spectral sequence and showed that, under certain condi…
Centralizers in good groups are good
Tobias Barthel, Nathaniel Stapleton
We modify the transchromatic character maps to land in a faithfully flat extension of Morava E-theory. Our construction makes use of the interaction between topological and algebra…