Partial Frobenius structures, Tate’s conjecture, and BSD over function fields.
Jared Weinstein (Boston University)
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
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