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In this talk we we explain a conjecture of Serre on genus
three curves over finite fields. We then describe a strategy
for solving this conjecture via the use of Jacobian varieties
and the Torelli theorem.
Unfortunately, this strategy fails to work due to the fact that Jacobians of genus three curves can have twists which are not themselves Jacobians. We explain how a Siegel modular form of degree on the Siegel upperhalf space of degree 3 can be used to distinguish between a Jacobian and its twist. After the seminar we will take the speaker to lunch. See the Algebra Seminar web page for information about other seminars in the series. Anthony Henderson anthonyh@maths.usyd.edu.au. |