Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T13:42:39.874Z Has data issue: false hasContentIssue false
  • English
  • Français

Kummer theory for big Galois representations

Published online by Cambridge University Press:  10 April 2007

DANIEL DELBOURGO  and
PAUL SMITH
DANIEL DELBOURGO
Affiliation:
Department of Mathematics, University Park, Nottingham, NG7 2RD. e-mail: [email protected], [email protected]
PAUL SMITH
Affiliation:
Department of Mathematics, University Park, Nottingham, NG7 2RD. e-mail: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In their 1990 paper, Bloch and Kato described the image of the Kummer map on an abelian variety over a local field, as the group of 1-cocycles which trivialise after tensoring by Fontaine's mysterious ring BdR. We prove the analogue of this statement for the universal nearly-ordinary Galois representation. The proof uses a generalisation of the Tate local pairing to representations over affinoid K-algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 205 - 217
Copyright
Copyright © Cambridge Philosophical Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[BK] Bloch, S. and Kato, K.. L-functions and Tamagawa numbers of motives. In the Grothendieck Festchrift I. Progr. Math. 86 (1990), 333–400.Google Scholar
[CM] Coleman, R. and Mazur, B.. The Eigencurve. LMS Lecture Notes Series 254 (1998), 1–113.Google Scholar
[Db] Delbourgo, D.. Super Euler systems and ordinary deformations of modular symbols. Preprint (2004).Google Scholar
[FM] Fontaine, J.-M. and Messing, W.. p-adic periods and p-adic étale cohomology. Contemp. Math. 67 (1987), 179–207.CrossRefGoogle Scholar
[GS] Greenberg, R. and Stevens, G.. p-adic L-functions and p-adic periods of modular forms. Invent. Math. 111 (1993), 401–447.CrossRefGoogle Scholar
[H1] Hida, H.. Galois representations into GL2( p [[X]]) attached to ordinary cusp forms. Invent. Math. 85 (1986), 545–613.CrossRefGoogle Scholar
[H2] Hida, H.. Iwasawa modules attached to congruences of cusp forms. Ann. Sci. École Norm. Sup. (4) 19 (1986), 231–273.CrossRefGoogle Scholar
[IS] Iovita, A. and Stevens, G.. p-adic variation of p-adic periods of modular forms. Preprint (2003).Google Scholar
[MW] Mazur, B. and Wiles, A.. On p-adic analytic families of Galois representations. Compositio Math. 59 (1986), 231–264.Google Scholar
[Sm] Smith, P.. PhD Thesis, University of Nottingham (2006).Google Scholar
[Ts] Tsuzuki, N.. The overconvergence of étale φ-∇-spaces on a local field. Compositio Math. 103 (1996), 227–239.Google Scholar