## STNB2018 (32nd edition)

### Howard's Big Heegner points

#### Presenters

Santiago Molina Blanco

#### Abstract

In this talk, we will describe how to put the Heegner points in families, namely, we will explain Howard's construction of big Heegner points. We will define a sequence of compatible points $P_s$ in the tower of modular curves $X_1(N p^s)$, where each $P_s$ has complex multiplication by an order of conductor $p^s$. These points define classes in the cohomology of the tower of modular curves through the Kummer map, hence they provide a class in the projective limit of the cohomology of the tower. The big Heegner point is the projection of such a class to the isotypical component associated with a given Hida family. Finally, we will explain Castellà's result that relates the specialization of a big Heegner point at higher weights $2k$ with the generalized Heegner cycles introduced in the second talk.