On the field generated by the periods of a Drinfeld module

2019/05/27 by Gekeler, Ernst-Ulrich
#11G09 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.11432

Abstract

Generalizing the results of Maurischat in \citeMaurischatxx, we show that the field K_∞(Λ) of periods of a Drinfeld module ϕ of rank r defined over K_∞ = \mathdsF_q((T^-1)) may be arbitrarily large over K_∞. We also show that, in contrast, the residue class degree f( K_∞(Λ) | K_∞) remains bounded by a constant that depends only on r.

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