2016/12/19 by David Burns, Burns, David, Takamichi Sano +1
Mathematics · Arts and Humanities · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Historical Studies and Socio-cultural Analysis
paper · pdf · doi:10.48550/arxiv.1612.06187
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.