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 (4). pp. 919-936. ISSN 0034-5318,
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For a smooth and proper variety Y over a finite field k the reciprocity map rho(Y) : CH0(Y) -> pi(ab)(1) (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 description 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 theorem. Furthermore, we give a new criterion for the injectivity of the reciprocity map for proper simple normal crossing varieties over finite fields.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; higher dimensional class field theory; reciprocity map; abelianized fundamental group; Seifert-van Kampen theorem; simple normal crossing varieties over finite fields |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Uwe Jannsen |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 May 2020 06:13 |
| Last Modified: | 04 May 2020 06:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17724 |
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