Optimal quotients of Jacobians with toric reduction and component groups
Number Theory
2019-08-15 v2
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.
Keywords
Cite
@article{arxiv.1212.3574,
title = {Optimal quotients of Jacobians with toric reduction and component groups},
author = {Mihran Papikian and Joseph Rabinoff},
journal= {arXiv preprint arXiv:1212.3574},
year = {2019}
}
Comments
19 pages. Reorganization and many edits; new proofs of Theorems 4.2 and 4.6