English

Resolution of Singularities of Arithmetical Threefolds II

Algebraic Geometry 2019-01-09 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1412.0868,
  title  = {Resolution of Singularities of Arithmetical Threefolds II},
  author = {Vincent Cossart and Olivier Piltant},
  journal= {arXiv preprint arXiv:1412.0868},
  year   = {2019}
}

Comments

updates and extends 'Resolution of Singularities of Arithmetical Threefolds I' posted on this website