Francesc Castella (Princeton)
Heegner cycles and p-adic L-functions

Abstract: Big Heegner points are cohomology classes attached to Hida families which are known to p-adically interpolate Heegner cycles for varying weights. About ten years ago, Howard (who originally constructed these classes) conjectured that big Heegner points are non-torsion over the Hida-Hecke algebra, and showed how his conjecture implies Greenberg's conjecture on the generic rank of Selmer groups in (self-dual twists of) Hida families. In this talk, I will explain the proof of a converse to Howard's theorem (joint work in progress with Chris Skinner), and describe the implications of this result to Greenberg's conjecture on the generic order of vanishing at the center of the p-adic L-functions attached to Hida families.