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

  • Patrick Forré

    Universität Regensburg, Germany

Abstract

For a smooth and proper variety over a finite field the reciprocity map 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