Zeta functions

December 1-5, 2008, Moscow, Russia




Practical details


Sergey Rybakov
Independent University of Moscow, Russia
rybakov.sergey (at) gmail.com

Zeta functions of genus 3 curves over finite fields

We will give some necessary and some sufficient conditions for a function to be a zeta function of genus 3 curve. To prove the result we have to con- struct an irreducible principal polarisation on an abelian threefold. Mostly we will discuss polarisations on abelian threefolds isogenous to a product of a geometrically simple abelian surface and an ordinary elliptic curve.

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