  We prove an adelic descent result for localizing invariants: for each
Noetherian scheme $X$ of finite Krull dimension and any localizing invariant
$E$, e.g., algebraic K-theory of Bass-Thomason, there is an equivalence
$E(X)\simeq \lim E(A^{\cdot}_{\text{red}}(X))$, where
$A^{\cdot}_{\text{red}}(X)$ denotes Beilinson's semi-cosimplicial ring of
reduced adeles on $X$. We deduce the equivalence from a closely related cubical
descent result, which we prove by establishing certain exact sequences of
perfect module categories over adele rings.
