Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

The theory of Coleman power series for $K_2$


Author: Takako Fukaya
Journal: J. Algebraic Geom. 12 (2003), 1-80
DOI: https://doi.org/10.1090/S1056-3911-02-00324-7
Published electronically: August 5, 2002
MathSciNet review: 1948685
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Abstract | References | Additional Information

Abstract: The purpose of this paper is to define ``Coleman power series'' associated to norm compatible systems in $K_2$ groups of complete discrete valuation fields of mixed characteristic $(0,p)$ with imperfect residue fields ${\mathsf{k}}$ such that $[{\mathsf {k}}:{\mathsf {k}}^p]=p$. These ``Coleman power series'' are elements of $K_2$groups of certain power series rings. We use our ``Coleman power series'' to obtain some results on modular forms, and we also study properties of our ``Coleman power series''.


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Additional Information

Takako Fukaya
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Email: takako@ms357.ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S1056-3911-02-00324-7
Received by editor(s): August 3, 2000
Published electronically: August 5, 2002

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