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arXiv · 1805.08448

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

David Burns·Ryotaro Sakamoto·Takamichi Sano
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Abstract

We prove the existence of a canonical `higher Kolyvagin derivative' homomorphism between the modules of higher rank Euler systems and higher rank Kolyvagin systems, as has been conjectured to exist by Mazur and Rubin. This homomorphism exists in the setting of $p$-adic representations that are free with respect to the action of a Gorenstein order $\mathcal{R}$ and, in particular, implies that higher rank Euler systems control the $\mathcal{R}$-module structures of Selmer modules attached to the representation. We give a first application of this theory by considering the (conjectural) Euler system of Rubin-Stark elements.

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David Burns, Ryotaro Sakamoto, Takamichi Sano. 2018-05-22. On the theory of higher rank Euler, Kolyvagin and Stark systems, II. https://arxiv.org/abs/1805.08448

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