Resolution of singularities of threefolds in mixed characteristic: case of small multiplicity

Vincent Cossart (1) , Olivier Piltant (1)

1 LMV - Laboratoire de Mathématiques de Versailles

This article is part of the authors' program on Resolution of Singularities of threefolds in mixed characteristic. We prove Local Uniformization for rank one valuations centered in a reduced hypersurface singularity $(X,x)\subset (Z,x)$, $Z$ any regular excellent fourfold, under the following assumption: $X$ has multiplicity smaller than the residue characteristic of $Z$. This is obtained by blowing up regular centers which are locally Hironaka permissible at the center of the valuation.

Mots clés: valuations; local uniformization; Zariski; arithmetic varieties

Domaines: Géométrie algébrique [math.AG]

Vincent Cossart, Olivier Piltant. Resolution of singularities of threefolds in mixed characteristic: case of small multiplicity. 2012. ⟨hal-00735929⟩