On v-adic periods of t-motives

TL;DR

This paper establishes a fundamental link between v-adic periods of t-motives and their Galois groups, leading to new results on the algebraic independence of formal polylogarithms over function fields.

Contribution

It proves the equality between the transcendental degree of v-adic periods and the dimension of the Galois group for t-motives, a novel result in the field.

Findings

Proved the equality between transcendental degree and Galois group dimension.

Established algebraic independence of certain formal polylogarithms.

Connected v-adic periods with Galois theory in function field arithmetic.

Abstract

In this paper, we prove the equality between the transcendental degree of the field generated by the v-adic periods of a t-motive M and the dimension of the Tannakian Galois group for M, where v is a "finite" place of the rational function field over a finite field. As an application, we prove the algebraic independence of certain "formal" polylogarithms.