Skip to main content\(\def\AAA{\mathbb{A}}
\def\CC{\mathbb{C}}
\def\FF{\mathbb{F}}
\def\NN{\mathbb{N}}
\def\QQ{\mathbb{Q}}
\def\RR{\mathbb{R}}
\def\TT{\mathbb{T}}
\def\ZZ{\mathbb{Z}}
\def\GG{\mathbf{G}}
\def\PP{\mathbf{P}}
\def\frakm{\mathfrak{m}}
\def\calA{\mathscr{A}}
\def\calB{\mathscr{B}}
\def\calC{\mathscr{C}}
\def\calD{\mathscr{D}}
\def\calF{\mathscr{F}}
\def\calL{\mathscr{L}}
\def\calM{\mathscr{M}}
\def\calO{\mathscr{O}}
\def\llbracket{[\![}
\def\rrbracket{]\!]}
\def\solid{\blacksquare}
\def\liquid{\approx}
\def\gas{\bigodot}
\DeclareMathOperator{\acc}{acc}
\DeclareMathOperator{\an}{an}
\DeclareMathOperator{\AnSpec}{AnSpec}
\DeclareMathOperator{\bd}{bd}
\DeclareMathOperator{\cof}{cof}
\DeclareMathOperator{\coker}{coker}
\DeclareMathOperator{\colim}{colim}
\DeclareMathOperator{\cond}{cond}
\DeclareMathOperator{\cone}{cone}
\DeclareMathOperator{\Cts}{Cts}
\DeclareMathOperator{\dg}{dg}
\DeclareMathOperator{\disc}{disc}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Ext}{Ext}
\DeclareMathOperator{\fin}{fin}
\DeclareMathOperator{\fpqc}{fpqc}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\ima}{image}
\DeclareMathOperator{\MaxSpec}{MaxSpec}
\DeclareMathOperator{\op}{op}
\DeclareMathOperator{\Proj}{Proj}
\DeclareMathOperator{\red}{red}
\DeclareMathOperator{\seq}{seq}
\DeclareMathOperator{\sheaf}{sheaf}
\DeclareMathOperator{\sing}{sing}
\DeclareMathOperator{\Spa}{Spa}
\DeclareMathOperator{\Spv}{Spv}
\DeclareMathOperator{\Spec}{Spec}
\DeclareMathOperator{\spect}{sp}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\Ab}{\mathbf{Ab}}
\DeclareMathOperator{\AnRing}{\mathbf{AnRing}}
\DeclareMathOperator{\AnStack}{\mathbf{AnStack}}
\DeclareMathOperator{\CAb}{\mathbf{CAb}}
\DeclareMathOperator{\Ch}{\mathbf{Ch}}
\DeclareMathOperator{\CHaus}{\mathbf{CHaus}}
\DeclareMathOperator{\CSet}{\mathbf{CSet}}
\DeclareMathOperator{\iExt}{\underline{Ext}}
\DeclareMathOperator{\Fun}{\mathbf{Fun}}
\DeclareMathOperator{\iHom}{\underline{Hom}}
\DeclareMathOperator{\LCAb}{\mathbf{LCAb}}
\DeclareMathOperator{\LCRS}{\mathbf{LCRS}}
\DeclareMathOperator{\LQCoh}{\mathbf{LQCoh}}
\DeclareMathOperator{\LRS}{\mathbf{LRS}}
\DeclareMathOperator{\Mod}{\mathbf{Mod}}
\DeclareMathOperator{\Prof}{\mathbf{Prof}}
\DeclareMathOperator{\Ring}{\mathbf{Ring}}
\DeclareMathOperator{\Sch}{\mathbf{Sch}}
\DeclareMathOperator{\Set}{\mathbf{Set}}
\DeclareMathOperator{\Shv}{\mathbf{Shv}}
\DeclareMathOperator{\Top}{\mathbf{Top}}
\DeclareMathOperator{\TopAb}{\mathbf{TopAb}}
\DeclareMathOperator{\QCoh}{\mathbf{QCoh}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
