English

A short proof of smooth implies flat

Algebraic Geometry 2016-02-15 v3 Commutative Algebra

Abstract

Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.

Keywords

Cite

@article{arxiv.1504.05709,
  title  = {A short proof of smooth implies flat},
  author = {Jesús Conde-Lago},
  journal= {arXiv preprint arXiv:1504.05709},
  year   = {2016}
}

Comments

v2: minor changes; v3: slight improvements regarding v2

R2 v1 2026-06-22T09:20:19.759Z