Luca Mastella: CM points on Shimura curves and anticyclotomic Iwasawa theory of GL_2 abelian varieties


Number Theory Seminar: Luca Mastella (UniDistance Suisse)

CM points on Shimura curves and anticyclotomic Iwasawa theory of GL_2 abelian varieties 

I will report on a work in progress with Ahmed Matar and Francesco Zerman, which aims to generalize some results of Matar and Jan Nekovář on anticyclotomic Iwasawa theory of elliptic curves defined over Q to GL_2 “modular” abelian varieties over a totally real number field. In the talk I will explain how to achieve this aim applying a suitable version of Kolyvagin’s method to the Euler system of CM points on quaternionic Shimura curves.