Eisenstein degeneration of Euler systems

TL;DR

This paper explores the degeneration of Euler systems through Coleman families, establishing relations between various arithmetic objects and suggesting potential for constructing new Euler systems.

Contribution

It introduces a novel approach using Coleman families to analyze degeneration phenomena in Euler systems, linking multiple important arithmetic classes.

Findings

Relations between Kato elements, Beilinson--Flach classes, and diagonal cycles established.

Connections between Heegner cycles and elliptic units demonstrated.

Method suggests potential for constructing new Euler systems.

Abstract

We discuss the theory of Coleman families interpolating critical-slope Eisenstein series. We apply it to study degeneration phenomena at the level of Euler systems. In particular, this allows us to prove relations between Kato elements, Beilinson--Flach classes and diagonal cycles, and also between Heegner cycles and elliptic units. We expect that this method could be extended to construct new instances of Euler systems.