SMS scnews item created by Anthony Henderson at Fri 2 May 2008 1421
Type: Seminar
Distribution: World
Expiry: 9 May 2008
Calendar1: 9 May 2008 1205-1255
CalLoc1: Carslaw 373
CalTitle1: Algebra Seminar: Meagher -- Twists of genus three Jacobians

Algebra Seminar

Twists of genus three Jacobians

Stephen Meagher

9th May, 12:05-12:55pm, Carslaw 373


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

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