Resolution of Singularities of Arithmetical Threefolds II

Vincent Cossart (1) , Olivier Piltant (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We prove Grothendieck's Conjecture on Resolution of Singulari-ties for quasi-excellent schemes X of dimension three and of arbitrary characteristic. This applies in particular to X = SpecA, A a reduced complete Noetherian local ring of dimension three and to algebraic or arithmetical varieties of dimension three. Similarly, if F is a number field, a complete discretely valued field or more generally the quotient field of any excellent Dedekind domain O, any regular projective sur-face X/F has a proper and flat model X over O which is everywhere regular.

Mots clés: resolution of singularities; blowing up; arithmetical varieties; Zariski; Grothendieck; valuations; AMS Classification: 11G25; 11G35; 14B05; 14E15

Domaines: Géométrie algébrique [math.AG]

Vincent Cossart, Olivier Piltant. Resolution of Singularities of Arithmetical Threefolds II. Journal of Algebra, 2019, ⟨10.1016/j.jalgebra.2019.02.017⟩. ⟨hal-01089140v2⟩