Adelic Geometry and Polarity

TL;DR

This paper extends classical geometry of numbers results to the adelic setting of number fields by introducing a notion of polarity for adelic convex bodies, broadening the scope of transference theorems.

Contribution

It introduces a new concept of polarity for adelic convex bodies and generalizes transference theorems to the adelic geometry of numbers.

Findings

Established a notion of polarity for adelic convex bodies.

Generalized classical transference theorems to adelic geometry.

Provided foundational tools for further research in adelic convex geometry.

Abstract

In the present paper we generalise transference theorems from the classical geometry of numbers to the geometry of numbers over the ring of adeles of a number field. To this end we introduce a notion of polarity for adelic convex bodies.