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# Jeff Achter : Divisibility of the number of points on Jacobians

Given an elliptic curve over a finite field, one might reasonably ask for the chance that it has a rational point of order $\ell$. More generally, what is the chance that a curve drawn from a family over a finite field has a point of order $\ell$ on its Jacobian? The answer is encoded in an $\ell$-adic representation associated to the family in question. In this talk, I'll answer this question for hyper- or trielliptic curves, and give some results concerning an arbitrary family of curves. ** Keeping in mind what you said about the audience, I'll focus on the geometric and topological ideas.

**Category**: Algebraic Geometry**Duration**: 01:34:59**Date**: April 5, 2006 at 4:25 PM-
**Tags:**seminar, Algebraic Geometry Seminar

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