**William A. Stein - Brian Conrad**

Suppose
is an optimal quotient of abelian varieties over
a -adic field, optimal in the sense that is connected.
Assume that is equipped with a symmetric principal
polarization (e.g., any Jacobian of a curve has such a
polarization), that has semistable reduction, and that has
purely toric reduction. In this paper, we express the group of
connected components of the Néron model of in terms of the
monodromy pairing on the character group of the torus associated
to . We apply our results in the case when is an optimal
quotient of the modular Jacobian . For each prime that
exactly divides , we obtain an algorithm to compute the component
group of at .

- Introduction
- The Main Results
- Optimal Quotients
- The Closed Fiber of the Néron Model
- The Degree of a Symmetric Isogeny
- Statement and Proof of the Main Theorem
- Optimal Quotients of
- Appendix: Some Facts Concerning Toric Reduction
- Bibliography
- About this document ...

William A Stein 2001-12-09