2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169914We 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.Slightly rewritten; appendix omitted; section added on the computation of motivic nearby cycles in terms of semi-stable modelsAlgebraic Geometrytext