Baker Theorem and Drinfeld Modules

Siegel’s Theorem for Drinfeld Modules

We prove a Siegel type statement for finitely generated φsubmodules of Ga under the action of a Drinfeld module φ. This provides a positive answer to a question we asked in a previous paper. We also prove an analog for Drinfeld modules of a theorem of Silverman for nonconstant rational maps of P over a number field.

The Mordell-lang Theorem for Drinfeld Modules

We study the quasi-endomorphism ring of certain infinitely definable subgroups in separably closed fields. Based on the results we obtain, we are able to prove a MordellLang theorem for Drinfeld modules of finite characteristic. Using specialization arguments we prove also a Mordell-Lang theorem for Drinfeld modules of generic characteristic.

Lehmer Inequality and the Mordell-weil Theorem for Drinfeld Modules

In this paper we prove a special case of the Lehmer inequality for Drinfeld modules which will enable us to extend the results of [6] and [8] to certain infinitely generated fields.

Drinfeld Modules and Elliptic Sheaves

Introduction to Drinfeld Modules

(1) Explicit class field theory for global function fields (just as torsion of Gm gives abelian extensions of Q, and torsion of CM elliptic curves gives abelian extension of imaginary quadratic fields). Here global function field means Fp(T ) or a finite extension. (2) Langlands conjectures for GLn over function fields (Drinfeld modular varieties play the role of Shimura varieties). (3) Modular...