Optimal quotients of Jacobians with toric reduction and component groups

Mihran Papikian, Joseph Rabinoff

Research output: Contribution to journalArticle

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 φJ → φE on component groups of the Neron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which φJ → φE E is surjective and discuss when these criteria hold for the Jacobians of modular curves.

Original languageEnglish (US)
Pages (from-to)1362-1381
Number of pages20
JournalCanadian Journal of Mathematics
Volume68
Issue number6
DOIs
StatePublished - Dec 2016

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Quotient
Jacobian Varieties
Modular Curves
Local Field
Elliptic Curves
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Optimal quotients of Jacobians with toric reduction and component groups. / Papikian, Mihran; Rabinoff, Joseph.

In: Canadian Journal of Mathematics, Vol. 68, No. 6, 12.2016, p. 1362-1381.

Research output: Contribution to journalArticle

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