On higher special elements of p-adic representations

2018/09/11 by David Burns, Burns, David, Takamichi Sano +3
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1809.03830

53 pages

arxiv created 2018/09/11 · arxiv updated 2018/09/12

Abstract

As a natural generalization of the notion of `higher rank Euler system', we develop a theory of `higher special elements' in the exterior power biduals of the Galois cohomology of p-adic representations. We show, in particular, that such elements encode detailed information about the structure of Galois cohomology groups and are related by families of congruences involving natural height pairings on cohomology. As a first concrete application of the approach, we use it to refine, and extend, a variety of existing results and conjectures concerning the values of derivatives of Dirichlet L-series.

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