Euler systems for $\mathrm{GSp}(4)$ over imaginary quadratic fields

TL;DR

This paper constructs an Euler system for GSp(4) automorphic representations over imaginary quadratic fields, providing new tools to bound Selmer groups and extend existing Euler systems to motivic contexts.

Contribution

It introduces a novel Euler system for GSp(4) over imaginary quadratic fields and extends previous work to include motivic interpretations and small weights.

Findings

Bounded strict Selmer groups using the Euler system

Extended GSp(4)×GL(2) Euler system to motivic statements

Provided a new construction applicable to general-type cohomological representations

Abstract

We construct an Euler system attached to general-type cohomological cuspidal automorphic representations of $\mathrm{GSp}(4)$ twisted by a Groessencharacter of an imaginary quadratic field. We then use this to bound strict Selmer groups under standard hypotheses. In addition, our approach gives a way of extending the $\mathrm{GSp}(4)\times\mathrm{GL}(2)$ Euler system of Hsu-Jin-Sakamoto to a motivic statement which also covers certain small weights omitted in op$.$cit.