The eisenstein ideal and jacquet-langlands isogeny over function fields

Mihran Papikian, Fu Tsun Wei

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let p and q be two distinct prime ideals of Fq[T]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curve X0(pq) to compare the rational torsion subgroup of the Jacobian J0(pq) 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.

Original languageEnglish (US)
Pages (from-to)551-630
Number of pages80
JournalDocumenta Mathematica
Volume20
Issue number2015
StatePublished - Jan 1 2015

Fingerprint

Isogeny
Function Fields
Subgroup
Isogenies
Modular Curves
Hecke Algebra
Prime Ideal
Divisor
Torsion
Analogue
Distinct

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{4e4cfccaaf2747eb914f2d17634b86c8,
title = "The eisenstein ideal and jacquet-langlands isogeny over function fields",
abstract = "Let p and q be two distinct prime ideals of Fq[T]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curve X0(pq) to compare the rational torsion subgroup of the Jacobian J0(pq) 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.",
author = "Mihran Papikian and Wei, {Fu Tsun}",
year = "2015",
month = "1",
day = "1",
language = "English (US)",
volume = "20",
pages = "551--630",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",
number = "2015",

}

The eisenstein ideal and jacquet-langlands isogeny over function fields. / Papikian, Mihran; Wei, Fu Tsun.

In: Documenta Mathematica, Vol. 20, No. 2015, 01.01.2015, p. 551-630.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The eisenstein ideal and jacquet-langlands isogeny over function fields

AU - Papikian, Mihran

AU - Wei, Fu Tsun

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Let p and q be two distinct prime ideals of Fq[T]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curve X0(pq) to compare the rational torsion subgroup of the Jacobian J0(pq) 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.

AB - Let p and q be two distinct prime ideals of Fq[T]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curve X0(pq) to compare the rational torsion subgroup of the Jacobian J0(pq) 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.

UR - http://www.scopus.com/inward/record.url?scp=84957962556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957962556&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84957962556

VL - 20

SP - 551

EP - 630

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

IS - 2015

ER -