Resolution of singularities of arithmetical threefolds

By Vincent Cossart, Olivier Piltant. Journal of Algebra, 2014

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

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