TY - JOUR
T1 - On Higher Special Elements of p-Adic Representations
AU - Burns, David
AU - Sano, Takamichi
AU - Tsoi, Kwok Wing
N1 - Publisher Copyright:
© 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].
PY - 2021/10/1
Y1 - 2021/10/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85122201244&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnz378
DO - 10.1093/imrn/rnz378
M3 - Article
AN - SCOPUS:85122201244
SN - 1073-7928
VL - 2021
SP - 15337
EP - 15411
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 20
ER -