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

Mihran Papikian; Fu Tsun Wei

doi:10.1007/s00209-016-1835-2

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

Mihran Papikian, Fu Tsun Wei

Mathematics

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3 Scopus citations

Abstract

Let n be a square-free ideal of F_q[ T]. We study the rational torsion subgroup of the Jacobian variety J₀(n) of the Drinfeld modular curve X₀(n). We prove that for any prime number ℓ not dividing q(q- 1) , the ℓ-primary part of this group coincides with that of the cuspidal divisor class group. We further determine the structure of the ℓ-primary part of the cuspidal divisor class group for any prime ℓ not dividing q- 1.

Original language	English (US)
Pages (from-to)	521-546
Number of pages	26
Journal	Mathematische Zeitschrift
Volume	287
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-016-1835-2
State	Published - Dec 26 2017

All Science Journal Classification (ASJC) codes

General Mathematics

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abstract = "Let n be a square-free ideal of Fq[ T]. We study the rational torsion subgroup of the Jacobian variety J0(n) of the Drinfeld modular curve X0(n). We prove that for any prime number ℓ not dividing q(q- 1) , the ℓ-primary part of this group coincides with that of the cuspidal divisor class group. We further determine the structure of the ℓ-primary part of the cuspidal divisor class group for any prime ℓ not dividing q- 1.",

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AU - Papikian, Mihran

AU - Wei, Fu Tsun

PY - 2017/12/26

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N2 - Let n be a square-free ideal of Fq[ T]. We study the rational torsion subgroup of the Jacobian variety J0(n) of the Drinfeld modular curve X0(n). We prove that for any prime number ℓ not dividing q(q- 1) , the ℓ-primary part of this group coincides with that of the cuspidal divisor class group. We further determine the structure of the ℓ-primary part of the cuspidal divisor class group for any prime ℓ not dividing q- 1.

AB - Let n be a square-free ideal of Fq[ T]. We study the rational torsion subgroup of the Jacobian variety J0(n) of the Drinfeld modular curve X0(n). We prove that for any prime number ℓ not dividing q(q- 1) , the ℓ-primary part of this group coincides with that of the cuspidal divisor class group. We further determine the structure of the ℓ-primary part of the cuspidal divisor class group for any prime ℓ not dividing q- 1.

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

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