Number Theory Seminar
New Constructions of Euler Systems via Eisenstein Series and the Cohomology of Shimura Varieties
Speaker: Fernando Trejos Suárez (Princeton)Date: Thursday, 18 June 2026 - 12:30Place: Aula Azul, ICMAT
Abstract:
Euler systems are a powerful tool for proving Iwasawa main conjectures. Euler systems are difficult to construct, though, and few examples exist. We will discuss applications of a new method for constructing Euler systems, first used by Sangiovanni and Skinner. To explain the key ideas, we reconstruct the two simplest Euler systems, the cyclotomic and ellìptic units (based on joint work with Shang and Skinner). The Euler system classes are defined as extensions of Galois representations within the étale cohomology of the modular curve relative to a collection of points. Afterwards, we discuss new applications of this method, including (time permitting) forthcoming work of the speaker to construct an Euler system for the " triple product" within the cohomology of the Siegel threefold.
