Partial Frobenius structures, Tate’s conjecture, and BSD over function fields.

Jared Weinstein (Boston University)

08-Jul-2020, 15:00-16:00 (4 years ago)

Abstract: Tate’s conjecture predicts that Galois-invariant classes in the $l$-adic cohomology of a variety are explained by algebraic cycles. It is known to imply the conjecture of Birch and Swinnerton-Dyer (BSD) for elliptic curves over function fields. When the variety, now assumed to be in characteristic p, admits a “partial Frobenius structure”, there is a natural extension of Tate’s conjecture. Assuming this conjecture, we get not only BSD, but the following result: the top exterior power of the Mordell-Weil group of an elliptic curve is spanned by a “Drinfeld-Heegner” point. This is a report on work in progress.

number theory

Audience: researchers in the topic


London number theory seminar

Series comments: For reminders, join the (very low traffic) mailing list at mailman.ic.ac.uk/mailman/listinfo/london-number-theory-seminar

For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html

Organizers: Caleb Springer*, Luis Garcia*
*contact for this listing

Export talk to