Tame class field theory for arithmetic schemes

URN to cite this document:: urn:nbn:de:bvb:355-epub-109860
DOI to cite this document:: 10.5283/epub.10986

Schmidt, Alexander

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Date of publication of this fulltext: 27 Nov 2009 06:52

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Item type:	Article
Journal or Publication Title:	Inventiones Mathematicae
Publisher:	Springer Verlag
Volume:	160
Number of Issue or Book Chapter:	3
Page Range:	527 -565
Date:	2005
Institutions:	Mathematics > Prof. Dr. Alexander Schmidt
Keywords:	class field theory; higher dimensional fields; arithmetic schemes; Chow group; zero cycles; fundamental group
Dewey Decimal Classification:	500 Science > 510 Mathematics
Status:	Published
Refereed:	Unknown
Created at the University of Regensburg:	Yes
Item ID:	10986

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Abstract

Takagi's class field theory gave a decription of the abelian extensions of a number field $K$ in terms of ideal groups in $K$. In the 1980s, {\it K. Kato} and {\it S. Saito} [``Global class field theory of arithmetic schemes". Applications of algebraic K-theory to algebraic geometry and number theory, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Boulder/Colo. 1983, Part I, Contemp. Math. 55, ...