Seminario

Seminario Teoría de Números

On the algebraic independence of Carlitz \(P\)-adic logarithms

Ponente:  Vincent Bosser (Université de Caen)
Fecha:  miércoles 30 de abril de 2025 - 14:30
Lugar:  Aula 420, Módulo 17, Departamento de Matemáticas, UAM

Resumen:

Let \(k={\mathbb F}_q(T)\). In 2008, Papanikolas proved that if Carlitz logarithms of elements of \(\bar{k}\) are linearly independent over \(k\), then they are algebraically independent over \(k\).
If \(P\in {\mathbb F}_q[T]\) is an irreducible polynomial, a similar statement can be made for Carlitz \(P\)-adic logarithms, but it still remains a conjecture. In this talk, we will present some partial results towards this conjecture.