Akhil Mathew (Harvard): Descent theorems in algebraic K-theory
In this talk, we will present some applications of the "transfer" to
algebraic K-theory, inspired by the work of Thomason. Let A --> B be
a G-Galois extension of rings, or more generally of E-infinity ring
spectra in the sense of Rognes. A basic question in algebraic
K-theory asks how close the map K(A) --> K(B)hG is to being an
equivalence, i.e., how close K is to satisfying Galois descent.
Motivated by the classical descent theorem of Thomason, one also
expects such a result after "periodic" localization. We formulate and
prove a general lemma that enables one to translate rational descent
statements as above into descent statements after telescopic
localization. As a result, we prove various descent results in the
telescopically localized K-theory, TC, etc. of ring spectra, and
verify several cases of a conjecture of Ausoni-Rognes. This is joint
work with Dustin Clausen, Niko Naumann, and Justin Noel.
Published Sep. 27, 2017 11:44 AM
- Last modified Sep. 27, 2017 11:44 AM