2007/10/01 by Johannes Nicaise, Nicaise, Johannes
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.0710.0330
Slightly rewritten; appendix omitted; section added on the computation of motivic nearby cycles in terms of semi-stable models
arxiv created 2008/09/26 · arxiv updated 2009/12/01
We constructed the analytic Milnor fiber is a non-archimedean model of the classical topological Milnor fibration. In the present paper, we describe the homotopy type of the analytic Milnor fiber in terms of a strictly semi-stable model, and we show that its singular cohomology coincides with the weight zero part of the mixed Hodge structure on the nearby cohomology. We give a similar expression for Denef and Loeser's motivic Milnor fiber in terms of a strictly semi-stable model.