Non-vanishing of Kolyvagin systems and Iwasawa theory
Prof. Francesc Castella
2023-06-05 14:00-15:00
MCM110&Online
Speaker: Prof. Francesc Castella (UCSB)Time: 14:00-15:00 June 5, 2023 (Monday)
Place: MCM110 & Online (Zoom ID: 616 523 0607 Password: mcm1234)
Title: Non-vanishing of Kolyvagin systems and Iwasawa theory
Abstract: Let E/Q be an elliptic curve, and p>2 a prime of good ordinary reduction. In 1991, Kolyvagin conjectured the non-triviality of a system of cohomology classes derived from Heegner points on E of varying conductors. The first major result towards Kolyvagin's conjecture is due to W. Zhang, who about ten years ago obtained a proof of the conjecture under certain ramification hypotheses on E[p] that have recently been largely relaxed by N. Sweeting. In this talk, I will explain a new proof of Kolyvagin's conjecture building on Iwasawa theoretic techniques and the work of Cornut-Vatsal. Our result (joint with A. Burungale, G. Grossi, and C. Skinner) treats the cases where E[p] is irreducible as a Galois module as well as the first cases where E admits a rational p-isogeny.
