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arXiv · 0906.4429

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

Charlotte Hardouin
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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.

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Charlotte Hardouin. 2009-06-24. Computation of the Galois groups occuring in M. Papanikolas's study of Carlitz logarithms. https://arxiv.org/abs/0906.4429

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