Model theory and decidability theory for adele rings

Por Angus Macintyre (Queen Mary, University of London) (Emeritus).

Abstract: To each number field K there is attached a locally compact ring A_K, the ring of adeles over K. This ring is built from the completions of K at equivalence classes of absolute values. These can be either p-adic or real, or complex. Harmonic analysis on the adeles is a fundamental technique in number theory (since the famous thesis of John Tate) .