An introduction to Euler systems

Abstract: The Birch–Swinnerton-Dyer conjecture and its generalization, the Bloch–Kato conjecture, predict a deep relationship between special values of $L$-functions and arithmetic invariants such as Selmer groups. One of the most powerful tools for studying these conjectures is the theory of Euler systems, which provides a mechanism for bounding Selmer groups using compatible families of cohomology classes. In this talk, I will give an introduction to the theory of Euler systems and explain how they arise naturally in the setting of automorphic forms and Shimura varieties. I will then discuss some new examples arising from unitary and Siegel Shimura varieties, where new phenomena related to the non-uniqueness of period integrals appear, and outline recent ideas for overcoming these difficulties in the construction of Euler systems.

algebraic geometrynumber theory

Audience: researchers in the topic

FGC-HRI-IPM Number Theory Webinars

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