Parametrization of virtually K-rational Drinfeld modules of rank two

2019/10/31 by Okumura, Yoshiaki
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.14284

Abstract

For an extension K/\mathbbF_q(T) of the rational function field over a finite field, we introduce the notion of virtually K-rational Drinfeld modules as a function field analogue of ℚ-curves. Our goal in this article is to prove that all virtually K-rational Drinfeld modules of rank two with no complex multiplication are parametrized up to isogeny by K-rational points of a quotient curve of the Drinfeld modular curve Y₀(\mathfrakn) with some square-free level \mathfrakn. This is an analogue of Elkies' well-known result on ℚ-curves.

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