Resolution of singularities of arithmetical threefolds
Copyright policy )Resolution of singularities of arithmetical threefolds
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.
updates and extends 'Resolution of Singularities of Arithmetical Threefolds I' posted on this website
14B05, resolution of singularities, 14E15, Global theory and resolution of singularities (algebro-geometric aspects), Zariski, Singularities in algebraic geometry, valuations, Grothendieck, Mathematics - Algebraic Geometry, AMS Classification: 11G25, arithmetical varieties, Varieties over finite and local fields, FOS: Mathematics, 11G35, 11G25, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Varieties over global fields, blowing up, Algebraic Geometry (math.AG)
14B05, resolution of singularities, 14E15, Global theory and resolution of singularities (algebro-geometric aspects), Zariski, Singularities in algebraic geometry, valuations, Grothendieck, Mathematics - Algebraic Geometry, AMS Classification: 11G25, arithmetical varieties, Varieties over finite and local fields, FOS: Mathematics, 11G35, 11G25, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Varieties over global fields, blowing up, Algebraic Geometry (math.AG)
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