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On the Theory of Higher Rank Euler, Kolyvagin and Stark Systems

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David Burns, Takamichi Sano

Original languageEnglish
Pages (from-to)10118-10206
Number of pages89
JournalInternational Mathematics Research Notices
Volume2021
Issue number13
DOIs
Published1 Jul 2021

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Publisher Copyright: © 2019 The Author(s). Published by Oxford University Press. All rights reserved.

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Abstract

Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and Stark systems over principal artinian rings and discrete valuation rings. 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.

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