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The Kernel of the Reciprocity Map of Simple Normal Crossing Varieties over Finite Fields

Forre, Patrick (2012) The Kernel of the Reciprocity Map of Simple Normal Crossing Varieties over Finite Fields. Publications of the Research Institute for Mathematical Sciences 48, pp. 919-936.

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For a smooth and proper variety Y over a finite field k the reciprocity map ρY:\CH0(Y)→π\ab1(Y) is injective with dense image. For a proper simple normal crossing variety this is no longer true in general. In this paper we give a discription of the kernel and cokernel of the reciprocity map in terms of homology groups of a complex filled with descent data using an algebraic Seifert-van-Kampen ...


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Item type:Article
Institutions:Mathematics > Prof. Dr. Uwe Jannsen
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Keywords:higher dimensional class field theory, reciprocity map, abelianized fundamental group, Seifert–van Kampen theorem, simple normal crossing varieties over finite fields
Dewey Decimal Classification:500 Science > 510 Mathematics
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:34263
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