Integral points for Drinfeld modules
نویسندگان
چکیده
منابع مشابه
Integral Points for Drinfeld Modules
We prove that in the backward orbit of a nonpreperiodic (nontorsion) point under the action of a Drinfeld module of generic characteristic there exist at most finitely many points S-integral with respect to another nonpreperiodic point. This provides the answer (in positive characteristic) to a question raised by Sookdeo in [26]. We also prove that for each nontorsion point z there exist at mos...
متن کاملEquidistribution and Integral Points for Drinfeld Modules
We prove that the local height of a point on a Drinfeld module can be computed by averaging the logarithm of the distance to that point over the torsion points of the module. This gives rise to a Drinfeld module analog of a weak version of Siegel’s integral points theorem over number fields and to an analog of a theorem of Schinzel’s regarding the order of a point modulo certain primes.
متن کاملTorsion Points in Families of Drinfeld Modules
Let Φ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for Φ for all λ. If there exist infinitely many λ ∈ K such that both a(λ) and b(λ) are torsion points for Φ, then we show that for each λ ∈ K, we have that a(λ) is torsion for Φ if and only if b(λ) is torsion for Φ. In the case a,b...
متن کاملSiegel’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.
متن کاملIntroduction 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...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2014
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.01.013