Number Theory Seminar: Nils Bruin
Topic
Explicit descent setups
Speakers
Details
Abstract
In modern language, Fermat's Descent Infini establishes that an elliptic curve has a Mordell-Weil group of rank 0. Since then, the method has been generalized to provide an upper bound on the rank of any elliptic curve and further work also allows the analysis of the Mordell-Weil group of Jacobians of many hyperelliptic curves. Reformulating work of Schaefer, we present a general framework, in principle applicable to any curve, which allows us, under certain technical conditions, to provide an upper bound on the rank of the Jacobian of any curve. In particular, we have been able to compute some rank bounds on Jacobians of smooth plane quartic curves. This is joint work with Bjorn Poonen and Michael Stoll.
In modern language, Fermat's Descent Infini establishes that an elliptic curve has a Mordell-Weil group of rank 0. Since then, the method has been generalized to provide an upper bound on the rank of any elliptic curve and further work also allows the analysis of the Mordell-Weil group of Jacobians of many hyperelliptic curves. Reformulating work of Schaefer, we present a general framework, in principle applicable to any curve, which allows us, under certain technical conditions, to provide an upper bound on the rank of the Jacobian of any curve. In particular, we have been able to compute some rank bounds on Jacobians of smooth plane quartic curves. This is joint work with Bjorn Poonen and Michael Stoll.
Additional Information
Location: ASB 10900 (IRMACS - SFU Campus)
For more information please visit UBC Mathematics Department
Nils Bruin