Mathematics - Joint Algebra and Topology Seminar, Francesc Castella -Kolyvagin's conjecture
This event is in the past.
When:
December 12, 2023
1 p.m. to 2 p.m.
1 p.m. to 2 p.m.
Where:
Event category:
Seminar
In-person
Speaker: Francesc Castella
Institution: University of California, Santa Barbara
Title: Kolyvagin's conjecture and its refinements
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 obtained a proof of the conjecture under certain ramification hypotheses on E[p]. 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 treats the cases where E[p] is irreducible as a Galois module (with no ramification hypotheses) as well as the first cases where E admits a rational p-isogeny. Moreover, by the same methods we also prove a refinement of Kolyvagin's conjecture posed by W. Zhang in 2014. Based on a joint work with A. Burungale, G. Grossi, and C. Skinner.
Time: Tuesday, December 12, 1-2 pm.
Location: Nelson Room, FAB