# Component Groups of Purely Toric Quotients of Semistable Jacobians

**Abstract**

Suppose pi:J---->A is an optimal quotient of abelian varieties over
a p-adic field, optimal in the sense that ker(pi) is connected.
Assume that J is the Jacobian of a curve, that J has semistable
reduction, and that A has purely toric reduction. In this paper, we
express the group of connected components of the Neron model of A
in terms of the monodromy pairing on the character group of the torus
associated to J. We apply our results in the case when A is the
optimal quotient of J_{0}(N) attached to a newform. For each
prime p that exactly divides N, we obtain a computable formula for
the order of the component groups of A at p.

This paper has appeared in the Math Research Letters

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