JournalsprimsVol. 48, No. 4pp. 919–936

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

  • Patrick Forré

    Universität Regensburg, Germany
The Kernel of the Reciprocity Map of Simple Normal Crossing Varieties over Finite Fields cover
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Abstract

For a smooth and proper variety YY over a finite field kk the reciprocity map ρY:\CH0(Y)π1\ab(Y)\rho^Y: \CH_0(Y) \to \pi_1^\ab(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 theorem. Furthermore, we give a new criterion for the injectivity of the reciprocity map for proper simple normal crossing varieties over finite fields.

Cite this article

Patrick Forré, The Kernel of the Reciprocity Map of Simple Normal Crossing Varieties over Finite Fields. Publ. Res. Inst. Math. Sci. 48 (2012), no. 4, pp. 919–936

DOI 10.2977/PRIMS/91