Component Groups of Purely Toric Quotients of Semistable Jacobians

Brian Conrad ([email protected]) and William A. Stein



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 J0(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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