Number Theory Seminar

We construct a new anticyclotomic Euler system for the Galois representation attached to a modular form of weight 2k, twisted by an anticyclotomic Hecke character \chi of infinity type (m,-m), denoted V_{f,\chi}, when the Heegner hypothesis is not satisfied and m\ge k. If time permits, we will then show some arithmetic applications (in a joint work with F. Castella) of the constructed Euler system, including evidence of the Bloch-Kato Conjecture and the Iwasawa Main Conjecture for V{f,\chi}.