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*}

105 Desirables

  • Section 105.1: Introduction
  • Section 105.2: Conventions
  • Section 105.3: Sites and Topoi
  • Section 105.4: Stacks
  • Section 105.5: Simplicial methods
  • Section 105.6: Cohomology of schemes
  • Section 105.7: Deformation theory √† la Schlessinger
  • Section 105.8: Definition of algebraic stacks
  • Section 105.9: Examples of schemes, algebraic spaces, algebraic stacks
  • Section 105.10: Properties of algebraic stacks
  • Section 105.11: Lisse √©tale site of an algebraic stack
  • Section 105.12: Things you always wanted to know but were afraid to ask
  • Section 105.13: Quasi-coherent sheaves on stacks
  • Section 105.14: Flat and smooth
  • Section 105.15: Artin's representability theorem
  • Section 105.16: DM stacks are finitely covered by schemes
  • Section 105.17: Martin Olsson's paper on properness
  • Section 105.18: Proper pushforward of coherent sheaves
  • Section 105.19: Keel and Mori
  • Section 105.20: Add more here