28 citations · 105 across the 29 of their papers we have counts for
5 papers · 1 filter
-adic heights of Heegner points and Beilinson-Flach elements
Francesc Castella
We give a new proof of Howard's -adic Gross-Zagier formula, which we extend to the context of indefinite Shimura curves over attached to nonsplit quaternion algebra…
On the exceptional specializations of big Heegner points
Francesc Castella
We extend the -adic Gross-Zagier formula of Bertolini, Darmon, and Prasanna to the semistable non-crystalline setting, and combine it with our previous work to obtain a derivati…
Iwasawa Main Conjecture for Heegner Points: Supersingular Case
Francesc Castella, Xin Wan
In this paper we propose and prove an anticyclotomic Iwasawa main conjecture for Heegner points on supersingular elliptic curves with . The result has a "" nature in th…
Heegner cycles and -adic -functions
Francesc Castella, Ming-Lun Hsieh
In this paper, we deduce the vanishing of Selmer groups for the Rankin-Selberg convolution of a cusp form with a theta series of higher weight from the nonvanishing of the associat…
Variation of anticyclotomic Iwasawa invariants in Hida families
Francesc Castella, Chan-Ho Kim, Matteo Longo
Building on the construction of big Heegner points in the quaternionic setting, and their relation to special values of Rankin-Selberg -functions, we obtain anticyclotomic analo…