Pierrick Gaudry
Ecole polytechnique, Paris
Counting points of genus 2 curves over finite fields
Thursday 15 March, 3-4pm
Eastern Avenue Tutorial Room 404
Let C be a curve of genus 2 over a finite field for which we want
to find the number of points. This problem can be reduced to
counting points on the Jacobian of C, which is easier, due to its
group structure.
After recalling some basics about these objects, we will describe
a Schoof-like algorithm which gives a solution to our problem in
polynomial runtime and has been implemented in Magma.
Still, this algorithm is not yet enough to treat large
examples and the natural question is how to extend to the genus 2
the methods of Elkies-Atkin which have proved to be efficient for
elliptic curves. We will present a construction of some modular
equations that can be useful in this context.
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