STNB2018 (32nd edition)

Howard's Big Heegner points


Santiago Molina Blanco


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.


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