The Stacks project

\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

Bibliography entry GruRay

author
Gruson, Laurent and Raynaud, Michel
title
Critères de platitude et de projectivité
year
1971
journal
Invent. math.
volume
13
pages
1–89

@ARTICLE{GruRay,
    AUTHOR = "Gruson, Laurent and Raynaud, Michel",
    TITLE = "Crit\`{e}res de platitude et de projectivit\'{e}",
    JOURNAL = "Invent. math.",
    VOLUME = "13",
    YEAR = "1971",
    PAGES = "1--89"
}

      

This item is referenced in 17 tags:

  • in Section 10.79: Faithfully flat descent for projectivity of modules
  • in Section 28.26: Generic flatness
  • in Remark 28.26.3
  • in Section 36.40: Application to the structure of finite type morphisms
  • in Section 36.47: Descending separated locally quasi-finite morphisms, which cites Lemma 5.7.1 of GruRay
  • in Section 37.1: Introduction
  • in Section 37.4: One step dévissage
  • in Section 37.9: Projective modules
  • in Remark 37.9.4
  • in Section 37.16: Relatively pure modules
  • in Remark 37.16.2
  • in Section 37.25: Variants of a lemma, which cites Lemma 4.2.2 of GruRay
  • in Section 60.8: Stratifying algebraic spaces by schemes, which cites Proposition 5.7.8 of GruRay
  • in Lemma 60.8.6, which cites Proposition 5.7.8 of GruRay
  • in Section 67.9: Induction principle
  • in Section 69.1: Introduction
  • in Section 102.31: Finite type, not finitely presented, flat at prime, which cites Part I, Remarques (3.4.7) (v) of GruRay