Computation of the Galois groups occuring in M. Papanikolas's study of Carlitz logarithms - Mathematics > Number TheoryReport as inadecuate




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Abstract: In this note, we state a theorem of compution of the unipotent radical of theGalois group of an object $U$ of a tannakian category defined over a field ofpositive characteristic, extension of the unit object by a semi-simple one. Wethen give a criteria of algebricity of solutions of the objects in terms oflinear dependences in groups of extension. We apply these results to thetanakian framework of $t$-motives developped by M. Papanikolas; in particular,we give an alternative proof of the algebraic independence of Carlitzlogarithms.



Author: Charlotte Hardouin

Source: https://arxiv.org/



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