Adelic descent for K-theory

We prove an adelic descent result for localizing invariants: for each Noetherian scheme X of finite Krull dimension and any localizing in-variant E, e.g., algebraic K-theory of Bass-Thomason, there is an equivalence E(X) ? limE(A(red)((SIC))(X)), where A(red)((SIC))(X) denotes Beilinson's semi-cosimplicial ring of reduced adeles on X. We deduce the equivalence from a closely re-lated cubical descent result, which we prove by establishing certain exact se-quences of perfect module categories over adele rings.