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arXiv · 1910.00569

On non-abelian higher special elements of $p$-adic representations

Daniel Macias Castillo·Kwok-Wing Tsoi
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Abstract

We develop a theory of `non-abelian higher special elements' in the non-commutative exterior powers of the Galois cohomology of $p$-adic representations. We explore their relation to the theory of organising matrices and thus to the Galois module structure of Selmer modules. In concrete applications, we relate our general theory to the formulation of refined conjectures of Birch and Swinnerton-Dyer type and to the Galois structure of Tate-Shafarevich and Selmer groups of abelian varieties.

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Daniel Macias Castillo, Kwok-Wing Tsoi. 2019-10-01. On non-abelian higher special elements of $p$-adic representations. https://arxiv.org/abs/1910.00569

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