On the theory of higher rank Euler, Kolyvagin and Stark systems

TL;DR

This paper extends the theory of higher rank Euler, Kolyvagin, and Stark systems to more general coefficient rings and constructs a canonical module of such systems for a broad class of p-adic representations.

Contribution

It generalizes the existing theory to wider coefficient rings and constructs a canonical module of higher rank Euler systems for general p-adic representations.

Findings

Construction of a canonical module of higher rank Euler systems.

Extension of the theory to more general coefficient rings.

Proof that these systems relate to Kolyvagin and Stark systems under standard hypotheses.

Abstract

Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and Stark systems over principal artinian rings and discrete valuation rings. In this article we describe a natural extension of (a slightly modified version of) their theory to systems over more general coefficient rings. We also construct unconditionally, and for general $p$-adic representations, a canonical, and typically large, module of higher rank Euler systems and show that for $p$-adic representations satisfying standard hypotheses the image under a natural higher rank Kolyvagin-derivative type homomorphism of each such system is a higher rank Kolyvagin system that originates from a Stark system.