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

TL;DR

This paper establishes a Hasse local-global principle for polynomials with coefficients in Mordell-Weil type groups over number fields, extending classical number theory results to more complex algebraic structures.

Contribution

It proves a Hasse local-global principle for polynomials with coefficients in Mordell-Weil type groups over number fields, including S-units, abelian varieties, and algebraic K-theory groups.

Findings

Hasse local-global principle holds for S-units over number fields.

Hasse principle applies to abelian varieties with trivial endomorphism rings.

Results extend to odd algebraic K-theory groups.

Abstract

In this paper we prove Hasse local-global principle for polynomials with coefficients in Mordell-Weil type groups over number fields like S-units, abelian varieties with trivial ring of endomorphisms and odd algebraic K-theory groups.