Non-ordinary symmetric squares and Euler systems of rank 2
Abstract: I will report on joint work with A. Lei, D. Loeffler and G. Venkat, where we develop a signed-splitting procedure for non-integral Beilinson-Flach classes associated to the symmetric squares of p-non-ordinary forms. The novelty in this procedure is that it works even though the cyclotomic deformations of Beilinson-Flach classes do not possess an interpolation property that covers the full critical range. This is consistent with Perrin-Riou's conjectures on rank 2 Euler systems; as a matter of fact, our methods are inspired by the implications of her conjecture. In certain cases, A. Lei and I are able to prove that the integral classes we obtain indeed lift to a non-trivial rank 2 Euler system, confirming Perrin-Riou's predictions. This has applications to the Iwasawa theory of symmetric squares.