Computation of the Galois groups occuring in M. Papanikolas's study of Carlitz logarithms

2009/06/24 by Charlotte Hardouin, Hardouin, Charlotte
Computer Science · Engineering · Mathematics · #11D88 #11S20 #18E15 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11D88 #msc:11S20 #msc:18E15

paper · pdf · doi:10.48550/arxiv.0906.4429

Note (32/02/2007)-9 p

arxiv created 2009/06/24 · openalex publication_date 2009/06/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we state a theorem of compution of the unipotent radical of the Galois group of an object U of a tannakian category defined over a field of positive characteristic, extension of the unit object by a semi-simple one. We then give a criteria of algebricity of solutions of the objects in terms of linear dependences in groups of extension. We apply these results to the tanakian framework of t-motives developped by M. Papanikolas; in particular, we give an alternative proof of the algebraic independence of Carlitz logarithms.

Related

• On v-adic periods of t-motives
• Tannakian fundamental groups of blended extensions
• Galois descent for motivic theories
• Groupes de Galois motivques et périodes
• Tannakian Fundamental Groups Associated to Galois Groups