Description
Number theory seminar.
Speaker: Guhan Venkat.
Affiliation: Universite Laval, Quebec, Canada.
Date and Time: Friday 30 August, 2:30 pm - 3:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Stark-Heegner cycles for Bianchi modular forms.
Abstract: In his seminal paper in 2001, Henri Darmon proposed a systematic
construction of p-adic points on elliptic curves over the rational
numbers, viz. Stark–Heegner points. In this talk, I will report on the
construction of p-adic cohomology classes/cycles in the
Harris–Soudry–Taylor representation associated to a Bianchi cusp form,
building on the ideas of Henri Darmon and Rotger–Seveso. These local
cohomology classes are conjectured to be the restriction of global
cohomology classes in an appropriate Bloch–Kato Selmer group and have
consequences towards the Bloch–Kato–Beilinson conjecture as well as
Gross–Zagier type results. This is based on a joint work with Chris
Williams (Imperial College London).