A Lindemann-Weierstrass theorem for semiabelian varieties over function fields

TL;DR

This paper establishes a Lindemann-Weierstrass type theorem for semiabelian varieties over function fields, demonstrating algebraic independence of exponentials of certain algebraic points in this setting.

Contribution

It extends classical transcendence results to semiabelian varieties over function fields, focusing on differential algebraic relations and algebraic independence.

Findings

Proves an analogue of Lindemann-Weierstrass for semiabelian varieties over function fields.

Analyzes solutions to differential algebraic relations involving exponential maps.

Shows algebraic independence of exponentials in this new context.

Abstract

We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of Q-linearly independent algebraic numbers are algebraically independent) for commutative algebraic groups G without unipotent quotients, over function fields. We concentrate on solutions to the the differential algebraic relations satisfied by exp from LG to G.