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

2019/10/01 by Daniel Macias Castillo, Castillo, Daniel Macias, Kwok-Wing Tsoi +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1910.00569

Updated References

arxiv created 2022/01/19 · arxiv updated 2022/01/20

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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