### Abstract

Let p and q be two distinct prime ideals of F_{q}[T]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curve X_{0}(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 language | English (US) |
---|---|

Pages (from-to) | 551-630 |

Number of pages | 80 |

Journal | Documenta Mathematica |

Volume | 20 |

Issue number | 2015 |

State | Published - Jan 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Documenta Mathematica*,

*20*(2015), 551-630.

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*Documenta Mathematica*, vol. 20, no. 2015, pp. 551-630.

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

Research output: Contribution to journal › Article

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 -