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

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

2009-06-24

arxiv.org/abs/0906.4429v1

Mathematics

Number Theory

Note (32/02/2007)-9 p

Scientific paper

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.

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