Euler systems and relative cohomology
Christopher Skinner (Princeton University)
Abstract: Euler systems -- organized collections of Galois cohomology classes for arithmetically interesting p-adic Galois representations -- have been a useful tool for establishing the conjectured relation between special values of L-functions and the ranks and orders of Selmer groups when they exist. In this talk I will describe recent work providing new examples of Euler systems with cyclotomic variation, including an Euler system for the symmetric square of a modular form. As a replacement for the motivic origin of prior examples, we find the Galois extensions in the relative cohomology of Shimura varieties. The control needed to establish the norm relations and make connections with L-values is provided by recent results in integral p-adic Hodge theory, allowing explicit connection with holomorphic automorphic forms.
number theory
Audience: researchers in the topic
| Organizers: | Sol Friedberg*, Benjamin Howard, Dubi Kelmer, Spencer Leslie, Keerthi Madapusi Pera, Bjorn Poonen*, Andrew Sutherland*, Wei Zhang* |
| *contact for this listing |