Tohoku Mathematical Journal

A generalization of the theory of Coleman power series

Kazuto Ota

Full-text: Open access

Abstract

Shinichi Kobayashi found a generalization of the Coleman power series theory to formal groups of elliptic curves and applied it to a study of $p$-adic height pairings. In this paper, we generalize his theory of Coleman power series to general formal groups.

Article information

Source
Tohoku Math. J. (2), Volume 66, Number 3 (2014), 309-320.

Dates
First available in Project Euclid: 8 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1412783201

Digital Object Identifier
doi:10.2748/tmj/1412783201

Mathematical Reviews number (MathSciNet)
MR3266735

Zentralblatt MATH identifier
1314.14094

Subjects
Primary: 14L05: Formal groups, $p$-divisible groups [See also 55N22]
Secondary: 11S31: Class field theory; $p$-adic formal groups [See also 14L05] 11E95: $p$-adic theory 13F25: Formal power series rings [See also 13J05]

Keywords
Coleman power series formal group Dieudonné module

Citation

Ota, Kazuto. A generalization of the theory of Coleman power series. Tohoku Math. J. (2) 66 (2014), no. 3, 309--320. doi:10.2748/tmj/1412783201. https://projecteuclid.org/euclid.tmj/1412783201


Export citation

References

  • R. Coleman, Division values in local fields, Invent. Math. 53 (1979), 91–116.
  • J.-M. Fontaine, Groupes $p$-divisibles sur les corps locaux, Astérisque, No. 47–48, Société Mathématique de France, Paris, 1977.
  • T. Honda, On the theory of commutative formal groups, J. Math. Soc. Japan 22 (1970), 213–246.
  • H. Knospe, Iwasawa-theory of abelian varieties at primes of non-ordinary reduction, Manuscripta Math. 87 (1995), 225–258.
  • S. Kobayashi, Iwasawa theory for elliptic curves at supersingular primes, Invent. Math. 152 (2003), 1–36.
  • S. Kobayashi, The $p$-adic Gross-Zagier formula for elliptic curves at supersingular primes, Invent. Math. 191 (2013), 527–629.
  • B. Perrin-Riou, Théorie d'Iwasawa $p$-adique locale et globale, Invent. Math. 99 (1990), 247–292.
  • B. Perrin-Riou, Théorie d'Iwasawa des représentations $p$-adiques sur un corps local, Invent. Math. 115 (1994), 81–149.
  • J. Tate, $p$-divisible groups, Proc. Conf. Local Fields, 158–183, Springer, Berlin, 1967.