Explicit formulas for Drinfeld modules and their periods
نویسندگان
چکیده
منابع مشابه
Periods of Drinfeld modules and local shtukas with complex multiplication
Colmez [Col93] conjectured a product formula for periods of abelian varieties over number fields with complex multiplication and proved it in some cases. His conjecture is equivalent to a formula for the Faltings height of CM abelian varieties in terms of the logarithmic derivatives at s = 0 of certain Artin L-functions. In a series of articles we investigate the analog of Colmez’s theory in th...
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Let ρ be a Drinfeld A-module with generic characteristic defined over an algebraic function field. We prove that all of the algebraic relations among periods, quasiperiods, and logarithms of algebraic points on ρ are those coming from linear relations induced by endomorphisms of ρ.
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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.
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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...
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In analogy with the periods of abelian integrals of differentials of third kind for an elliptic curve defined over a number field, we introduce a notion of periods of third kind for a rank 2 Drinfeld Fq[t]-module ρ defined over an algebraic function field and derive explicit formulae for them. When ρ has complex multiplication by a separable extension, we prove the algebraic independence of ρlo...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2012.10.013