Luca Marannino (IMJ-PRG Paris)

In this talk we outline an approach to the study of anticyclotomic Iwasawa theory of modular forms when the fixed prime p is inert in the relevant quadratic imaginary field. Following ideas of Castella-Do and Alonso-Castella-Rivero for the “p split” case, one can envisage a construction of an anticyclotomic Euler system arising from a suitable manipulation of diagonal cycles (considered in previous works of Darmon-Rotger and Bertolini-Seveso-Venerucci). We will report on this work in progress, trying to underline the main difficulties arising in the “p inert” setting.