The Eisenstein ideal and Jacquet-Langlands isogeny over function fields

2013/06/16 by Mihran Papikian, Papikian, Mihran, Fu-Tsun Wei +1 · 1 citation
Mathematics · #11F12 #11G09 #11G18 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F12 #msc:11G09 #msc:11G18

paper · pdf · doi:10.48550/arxiv.1306.3632

71 pages. To appear in Documenta Mathematica

arxiv created 2015/05/26 · arxiv updated 2015/05/27

Abstract

Let \frakp and \frakq be two distinct prime ideals of \mathbbF_q[T]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curve X₀(\frakp\frakq) to compare the rational torsion subgroup of the Jacobian J₀(\frakp\frakq) with its subgroup generated by the cuspidal divisors, and to produce explicit examples of Jacquet-Langlands isogenies. Our results are stronger than what is currently known about the analogues of these problems over ℚ.

Cited by

• The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains

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• The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains
• On Jacquet-Langlands isogeny over function fields
• On maps between modular Jacobians and Jacobians of Shimura curves
• Rational torsion of generalised Drinfeld modular Jacobians of prime power level