\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*}

The Stacks project

Bibliography entry EGA

author
Dieudonné, Jean and Grothendieck, Alexander
title
Éléments de géométrie algébrique
year
1961–1967
journal
Inst. Hautes Études Sci. Publ. Math.
volume
4, 8, 11, 17, 20, 24, 28, 32

@ARTICLE{EGA,
    AUTHOR = "Dieudonn{\'e}, Jean and Grothendieck, Alexander",
    TITLE = "\'{E}l\'ements de g\'eom\'etrie alg\'ebrique",
    JOURNAL = "Inst. Hautes \'Etudes Sci. Publ. Math.",
    VOLUME = "4, 8, 11, 17, 20, 24, 28, 32",
    YEAR = "1961--1967"
}

      

This item is referenced in 83 tags:

  • in Section 10.36: Normal rings, which cites IV, 5.13.5 and 0, 4.1.4 of EGA
  • in Lemma 10.102.7, which cites Chapter 0, Proposition 16.5.4 of EGA
  • in Lemma 10.151.4: Serre's criterion for normality, which cites IV, Theorem 5.8.6 of EGA
  • in Definition 10.155.1, which cites Chapter 0, Definition 23.1.1 of EGA
  • in Lemma 10.155.16: Tate, which cites Theorem 23.1.3 of EGA
  • in Section 10.157: Ascending properties, which cites IV, Proposition 6.3.1 of EGA
  • in Lemma 10.157.1, which cites IV, Proposition 6.3.1 of EGA
  • in Lemma 15.44.3, which cites IV, Theorem 18.6.6 and Proposition 18.8.8 of EGA
  • in Section 17.1: Introduction
  • in Section 18.1: Introduction
  • in Section 25.1: Introduction
  • in Lemma 25.6.4, which cites II, Err 1, Prop. 1.8.1 of EGA
  • in Lemma 25.22.2: Valuative criterion separatedness, which cites II Proposition 7.2.3 of EGA
  • in Section 26.1: Introduction
  • in Section 26.8: Proj of a graded ring, which cites II, Section 2 of EGA
  • in Section 27.1: Introduction
  • in Section 27.7: Normal schemes, which cites 0, 4.1.4 of EGA
  • in Section 27.13: Japanese and Nagata schemes, which cites IV Corollary 5.11.4 of EGA
  • in Definition 27.26.1, which cites II Definition 4.5.3 of EGA
  • in Lemma 27.26.2, which cites II Proposition 4.5.6(i) of EGA
  • in Lemma 27.26.5, which cites II Proposition 4.5.6(ii) of EGA
  • in Section 28.1: Introduction
  • in Section 28.7: Scheme theoretic closure and density, which cites IV, Definition 11.10.2 of EGA
  • in Lemma 28.11.3, which cites II, Corollary 1.3.2 of EGA
  • in Definition 28.19.1, which cites II Definition 6.2.3 of EGA
  • in Lemma 28.22.5, which cites IV, Corollary 1.10.4 of EGA
  • in Lemma 28.27.4, which cites IV Theorem 13.1.3 of EGA
  • in Section 28.30: Conormal sheaf of an immersion, which cites IV Definition 16.1.2 of EGA
  • in Section 28.33: Unramified morphisms
  • in Definition 28.35.1, which cites II Definition 4.6.1 of EGA
  • in Lemma 28.35.4, which cites II, Proposition 4.6.3 of EGA
  • in Lemma 28.35.5, which cites II Corollary 4.6.6 of EGA
  • in Lemma 28.35.6, which cites II Proposition 5.1.6 of EGA
  • in Lemma 28.36.2, which cites II, Proposition 4.6.2 of EGA
  • in Section 28.38: Quasi-projective morphisms
  • in Definition 28.38.1, which cites II, Definition 5.3.1 of EGA
  • in Lemma 28.38.7, which cites II, Proposition 5.3.4 (i) of EGA
  • in Lemma 28.40.1: Valuative criterion for properness, which cites II Theorem 7.3.8 of EGA
  • in Section 28.41: Projective morphisms
  • in Section 29.1: Introduction
  • in Lemma 29.3.1, which cites II, Theorem 5.2.1 (d') and IV (1.7.17) of EGA
  • in Lemma 29.3.2, which cites II, Theorem 5.2.1 of EGA
  • in Lemma 29.8.1, which cites III Proposition 2.1.12 of EGA
  • in Lemma 29.17.1, which cites III Proposition 2.6.1 of EGA
  • in Lemma 29.18.1, which cites II Theorem 5.6.1(a) of EGA
  • in Proposition 29.19.1, which cites III Theorem 3.2.1 of EGA
  • in Section 29.24: Grothendieck's existence theorem, I
  • in Theorem 29.27.1: Grothendieck's existence theorem, which cites III Theorem 5.1.5 of EGA
  • in Section 30.1: Introduction
  • in Section 30.2: Associated points, which cites IV Definition 3.1.1 of EGA
  • in Section 30.4: Embedded points, which cites IV Definition 3.1.1 of EGA
  • in Section 30.18: Relative effective Cartier divisors, which cites IV, Section 21.15 of EGA
  • in Section 31.1: Introduction
  • in Lemma 31.4.2, which cites IV, Proposition 8.2.9 of EGA
  • in Proposition 31.6.1, which cites IV, Proposition 8.14.2 of EGA
  • in Section 31.11: Characterizing affine schemes, which cites II 6.7.1 of EGA
  • in Section 32.1: Introduction
  • in Lemma 32.7.13, which cites IV Corollary 4.5.13.1(i) of EGA
  • in Section 32.20: Algebraic schemes, which cites I Definition 6.4.1 of EGA
  • in Lemma 34.11.3, which cites IV, 17.7.5 (i) and (ii) of EGA
  • in Section 36.1: Introduction
  • in Theorem 36.15.1, which cites IV Theorem 11.3.1 of EGA
  • in Lemma 36.20.7, which cites IV Corollary 12.1.7(iii) of EGA
  • in Lemma 36.21.4, which cites IV Proposition 17.16.1 of EGA
  • in Lemma 36.38.3: Zariski's Main Theorem, which cites IV Corollary 18.12.13 of EGA
  • in Lemma 36.43.3, which cites IV Corollary 9.6.4 of EGA
  • in Lemma 36.46.9, which cites III, Proposition 5.5.1 of EGA
  • in Theorem 40.15.2: Une equivalence remarquable de catégories, which cites IV, Theorem 18.1.2 of EGA
  • in Section 48.14: Improving coherent modules
  • in Section 53.27: Affineness of complement of ramification locus, which cites Chapter IV, Section 21.12 of EGA
  • in Theorem 54.45.2, which cites IV Theorem 18.1.2 of EGA
  • in Section 68.5: Conormal sheaf of an immersion, which cites IV Definition 16.1.2 of EGA
  • in Section 79.1: Introduction
  • in Section 79.2: Formal schemes à la EGA
  • in Section 79.5: Affine formal algebraic spaces
  • in Remark 79.5.8
  • in Section 79.9: Completion along a closed subset, which cites Chapter I, Section 10.8 of EGA
  • in Remark 79.21.1: Universal property restricted power series, which cites Chapter 0, 7.5.3 of EGA
  • in Section 80.1: Introduction
  • in Section 91.3: The Hom functor, which cites III, Cor 7.7.8 of EGA
  • in Section 102.19: Non-quasi-affine variety with quasi-affine normalization, which cites II Remark 6.6.13 of EGA
  • in Section 102.36: A formally étale non-flat ring map, which cites 0, Example 19.10.3(i) of EGA
  • in Subsection 104.5.11: Theorem on formal functions and Grothendieck's Existence Theorem, which cites III.4.1.5 of EGA