Geodesic
The Eisenstein ideal and Jacquet-Langlands isogeny over function fields
Documenta mathematica, Tome 20 (2015), pp. 551-629
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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.
DOI : 10.4171/dm/499
Classification : 11F12, 11G09, 11G18
Mots-clés : Drinfeld modular curves, Eisenstein ideal, cuspidal divisor group, Shimura subgroup, Jacquet-Langlands isogeny 
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     author = {Mihran Papikian and Fu-Tsun Wei},
     title = {The {Eisenstein} ideal and {Jacquet-Langlands} isogeny over function fields},
     journal = {Documenta mathematica},
     pages = {551--629},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/499},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/499/}
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Mihran Papikian; Fu-Tsun Wei. The Eisenstein ideal and Jacquet-Langlands isogeny over function fields. Documenta mathematica, Tome 20 (2015), pp. 551-629. doi: 10.4171/dm/499

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