Optimal Quotients of Jacobians With ToricReduction and Component Groups

Papikian, Mihran ; Rabinoff, Joseph

Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1362-1381

Résumé

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.

Détail

DOI : 10.4153/CJM-2016-009-9

Mots-clés : 11G18, 14G22, 14G20, Jacobians with toric reduction, component groups, modular curves

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