On the arithmetic of polynomials with coefficients in Mordell-Weil type groups

Abstract

In this paper we prove the Hasse principle for polynomials with coefficients in Mordell-Weil type groups over number fields. Examples of such groups are (1) the groups of $S$-units in a number field, (2) abelian varieties with trivial ring of endomorphisms, and (3) odd algebraic $K$-theory groups.