English

Can a Drinfeld module be modular?

Number Theory 2007-05-23 v2 Algebraic Geometry

Abstract

Let kk be a global function field with field of constants \Fr\Fr and let \infty be a fixed place of kk. In his habilitation thesis \cite{boc2}, Gebhard B\"ockle attaches abelian Galois representations to characteristic pp valued cusp eigenforms and double cusp eigenforms \cite{go1} such that Hecke eigenvalues correspond to the image of Frobenius elements. In the case where k=\Fr(T)k=\Fr(T) and \infty corresponds to the pole of TT, it then becomes reasonable to ask whether rank 1 Drinfeld modules over kk are themselves ``modular'' in that their Galois representations arise from a cusp or double cusp form. This paper gives an introduction to \cite{boc2} with an emphasis on modularity and closes with some specific questions raised by B\"ockle's work.

Keywords

Cite

@article{arxiv.math/0210388,
  title  = {Can a Drinfeld module be modular?},
  author = {David Goss},
  journal= {arXiv preprint arXiv:math/0210388},
  year   = {2007}
}

Comments

Final corrected version