King's College London

Research portal

On Higher Special Elements of p-Adic Representations

Research output: Contribution to journalArticlepeer-review

David Burns, Takamichi Sano, Kwok Wing Tsoi

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

Bibliographical note

Publisher Copyright: © 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail:

King's Authors


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.

View graph of relations

© 2020 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454