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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
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

Received by editor(s): August 3, 2000
Published electronically: August 5, 2002