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On Higher Special Elements of p-Adic Representations

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David Burns, Takamichi Sano, Kwok Wing Tsoi

Original languageEnglish
Pages (from-to)15337-15411
Number of pages75
JournalInternational Mathematics Research Notices
Volume2021
Issue number20
DOIs
Published1 Oct 2021

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Abstract

As a natural generalisation 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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