On the log minimal model program for $3$-folds over imperfect fields of characteristic $p>5$

Omprokash Das; Joe Waldron

On the log minimal model program for $3$-folds over imperfect fields of characteristic $p>5$

Algebraic Geometry 2022-08-22 v3

Authors: Omprokash Das , Joe Waldron

Abstract

We prove that many of the results of the LMMP hold for $3$ -folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal rays, and the existence of log minimal models. As well as pertaining to the geometry of fibrations of relative dimension $3$ over algebraically closed fields, they have applications to tight closure in dimension $4$ .

Keywords

log minimal model program 3-folds imperfect fields characteristic p>5 flips cone theorem tight closure

Cite

@article{arxiv.1911.04394,
  title  = {On the log minimal model program for $3$-folds over imperfect fields of characteristic $p>5$},
  author = {Omprokash Das and Joe Waldron},
  journal= {arXiv preprint arXiv:1911.04394},
  year   = {2022}
}

Comments

Exposition simplified in section on field extensions. To appear in J. Lond. Math. Soc

On the log minimal model program for $3$-folds over imperfect fields of characteristic $p>5$

Abstract

Keywords

Cite

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