Geodesic
Optimal Quotients of Jacobians With ToricReduction and Component Groups
Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1362-1381

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DOI

Let $J$ be a Jacobian variety with toric reduction over a local field $K$ . Let $J\,\to \,E$ be an optimal quotient defined over $K$ , where $E$ is an elliptic curve. We give examples in which the functorially induced map ${{\Phi }_{J}}\,\to \,{{\Phi }_{E}}$ on component groups of the Néron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which ${{\Phi }_{J}}\,\to \,{{\Phi }_{E}}$ is surjective and discuss when these criteria hold for the Jacobians of modular curves.
DOI : 10.4153/CJM-2016-009-9
Mots-clés : 11G18, 14G22, 14G20, Jacobians with toric reduction, component groups, modular curves 
Papikian, Mihran; Rabinoff, Joseph. Optimal Quotients of Jacobians With ToricReduction and Component Groups. Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1362-1381. doi: 10.4153/CJM-2016-009-9
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     title = {Optimal {Quotients} of {Jacobians} {With} {ToricReduction} and {Component} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {1362--1381},
     year = {2016},
     volume = {68},
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     doi = {10.4153/CJM-2016-009-9},
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