An Euler system for GU(2, 1)

TL;DR

This paper constructs an Euler system linked to certain automorphic representations of GL(3) over imaginary quadratic fields, utilizing Shimura variety cohomology for GU(2, 1), advancing number theory and automorphic forms research.

Contribution

It introduces a novel Euler system construction for automorphic representations of GL(3) over imaginary quadratic fields, connecting Shimura varieties and Galois representations.

Findings

Established an Euler system for specific automorphic representations.

Connected Shimura variety cohomology to Galois representations.

Provided tools for studying special values and arithmetic of automorphic forms.

Abstract

We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of GL(3) over imaginary quadratic fields, using the cohomology of Shimura varieties for GU(2, 1).