Local-global problem for Drinfeld modules

2002/07/29 by G.J. van der Heiden, Gert-Jan van der Heiden, van der Heiden, Gert-Jan
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.NT

paper · pdf · doi:10.48550/arxiv.math/0207310

arxiv created 2002/07/29 · arxiv updated 2009/12/01

Abstract

Let K be a function field and let (f) be a principal prime ideal of the ring A, which is a subring of K. Let phi: A --> K tau be a Drinfeld module. In this paper we consider the problem whether a point P in K which is a phi(f)-fold locally at each place v of K, i.e., for each v there is a Q in K_v such that phi(f).P = Q, is also a phi(f)-fold globally. We also discuss the same problem in the context of elliptic curves, where it is much simpler.

Related

• Counterexamples to the local-global divisibility over elliptic curves
• The filled Julia set of a Drinfeld module and uniform bounds for torsion
• On a reduction map for Drinfeld modules
• On the Eisenstein ideal of Drinfeld modular curves
• On the Riemann Hypothesis for Drinfeld Modules