  Let $A \to B$ be a $G$-Galois extension of rings, or more generally of
$\mathbb{E}_\infty$-ring spectra in the sense of Rognes. A basic question in
algebraic $K$-theory asks how close the map $K(A) \to K(B)^{hG}$ is to being an
equivalence, i.e., how close algebraic $K$-theory is to satisfying Galois
descent. An elementary argument with the transfer shows that this equivalence
is true rationally in most cases of interest. Motivated by the classical
descent theorem of Thomason, one also expects such a result after periodic
localization.
  We formulate and prove a general result which enables one to promote rational
descent statements as above into descent statements after periodic
localization. This reduces the localized descent problem to establishing an
elementary condition on $K_0(-)\otimes \mathbb{Q}$. As applications, we prove
various descent results in the periodic localized $K$-theory, $TC$, $THH$, etc.
of structured ring spectra, and verify several cases of a conjecture of Ausoni
and Rognes.

K-Theory and Homology;Algebraic Topology