Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
ES Program Research Seminar: Non-Vanishing Of Kolyvagin Systems And Iwasawa Theory
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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.
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