\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*}
60 Decent Algebraic Spaces
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Section 60.1: Introduction
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Section 60.2: Conventions
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Section 60.3: Universally bounded fibres
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Section 60.4: Finiteness conditions and points
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Section 60.5: Conditions on algebraic spaces
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Section 60.6: Reasonable and decent algebraic spaces
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Section 60.7: Points and specializations
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Section 60.8: Stratifying algebraic spaces by schemes
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Section 60.9: Integral cover by a scheme
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Section 60.10: Schematic locus
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Section 60.11: Residue fields and henselian local rings
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Section 60.12: Points on decent spaces
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Section 60.13: Reduced singleton spaces
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Section 60.14: Decent spaces
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Section 60.15: Locally separated spaces
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Section 60.16: Valuative criterion
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Section 60.17: Relative conditions
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Section 60.18: Points of fibres
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Section 60.19: Monomorphisms
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Section 60.20: Generic points
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Section 60.21: Generically finite morphisms
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Section 60.22: Birational morphisms
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Section 60.23: Jacobson spaces
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Section 60.24: Local irreducibility
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Section 60.25: Catenary algebraic spaces