Hall 123

Stark-Heegner cycles for Bianchi modular forms

Guhan Venkat

Université Laval

In his seminal paper in 2001, Henri Darmon laid down a systematic construction of p-adic points, viz. Stark-Heegner points, on elliptic curves over the rational numbers. In this talk, I will report on the construction of p-adic cohomology classes/cycles in the Harris-Lan-Taylor-Thorne representation associated to a Bianchi cusp form, building on the ideas of Henri Darmon and Rotger-Seveso. These local cohomology classes are conjecturally 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).