Construction of an anticyclotomic Euler system with applications

Abstract

In this thesis, we construct a new anticyclotomic Euler system (in the sense of Jetchev-Nekovar-Skinner (JNS)) for the Galois representation attached to a newform f of weight 2k twisted by an anticyclotomic Hecke character \chi of infinity type (l,−l), denoted by V_f(\chi), when the Heegner Hypothesis is not satisfied. The main ingredients for our construction are the Bertolini-Seveso-Venerucci (BSV) diagonal classes and the Lei-Loeffler-Zerbes norm maps. We then show some arithmetic applications of the constructed Euler system, including the rank 0 Bloch-Kato Conjecture for V_f(\chi) when k>=l+1, using the explicit reciprocity law of BSV and the machinery of JNS.