157 citations · 749 across the 30 of their papers we have counts for
17 papers · 1 filter
Chromatic convergence for the algebraic K-theory of the sphere spectrum
Andrew J. Blumberg, Michael A. Mandell, Allen Yuan
We show that the map from to its chromatic completion is a connective cover and identify the fiber in -theoretic terms. We combine this with recent work of Land…
A version of Waldhausen's chromatic convergence for
Andrew J. Blumberg, Michael A. Mandell, Allen Yuan
The map is a weak equivalence.
The eigensplitting of the fiber of the cyclotomic trace for the sphere spectrum
Andrew J. Blumberg, Michael A. Mandell
Let be an odd prime. We show that the fiber sequence for the cyclotomic trace of the sphere spectrum admits an "eigensplitting" that generalizes known…
The strong Künneth theorem for topological periodic cyclic homology
Andrew J. Blumberg, Michael A. Mandell
Topological periodic cyclic homology (i.e., -Tate fixed points of ) has the structure of a strong symmetric monoidal functor of smooth and proper dg categories ove…
K-theoretic Tate-Poitou duality and the fiber of the cyclotomic trace
Andrew J. Blumberg, Michael A. Mandell
Let be an odd prime. We prove a spectral version of Tate-Poitou duality for the algebraic -theory spectra of number rings with inverted. This identifies th…
The homotopy groups of the algebraic K-theory of the sphere spectrum
Andrew J. Blumberg, Michael A. Mandell
We calculate , the homotopy groups of away from 2, in terms of the homotopy groups of , the homotopy groups of ${\mathbb C}P^\inf…