Yu-Sheng Lee: CM congruences and anticyclotomic Euler systems

Number theory seminar: Yu-Sheng Lee (University of Michigan)

CM congruences and anticyclotomic Euler systems

An Euler system is a collection of Galois cohomology classes satisfying certain norm relations, extensively used in studying the structure of Selmer groups since Kolyvagin's work on Heegner points on modular elliptic curves. On the other hand, Ribet's method and its generalizations show that when there are congruences between automorphic representations associated with Galois representations, one can often deform the Galois representation into an essentially irreducible family and obtain nontrivial Galois cohomology classes. In this talk, I will explain Urban's general framework for constructing Euler systems, which combines a systematic application of Ribet's method with input from p-adic local Langlands. I will then present a specific case involving the construction of anticyclotomic Euler systems associated with Hecke characters of CM fields and discuss their applications to Iwasawa theory.