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arXiv · 1212.3574

Optimal quotients of Jacobians with toric reduction and component groups

Mihran Papikian·Joseph Rabinoff
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Abstract

Let J be a Jacobian variety with toric reduction over a local field K. Let J -> 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 -> \Phi_E on component groups of the N\'eron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which \Phi_J -> \Phi_E is surjective, and discuss when these criteria hold for the Jacobians of modular curves.

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Mihran Papikian, Joseph Rabinoff. 2012-12-14. Optimal quotients of Jacobians with toric reduction and component groups. https://doi.org/10.4153/cjm-2016-009-9

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