\NeedsTeXFormat{LaTeX2e} \ProvidesPackage{abdoalias} %% Package Loading %% ==================================================== \RequirePackage{iftex} % do conditionals on tex engine \RequirePackage{suffix} % define starred commands \RequirePackage{amsmath} % AMS stuff \RequirePackage{amsfonts} % AMS fonts \RequirePackage{amssymb} % AMS symbols \RequirePackage{slashed} % Feynman slashes. % \RequirePackage{tensor} % Typeset tensor indices. % \RequirePackage{young} % Draw Young tableaux. \RequirePackage{stmaryrd} % Extra math symbols (like double square bracket) %% Font change shortcuts %% ==================================================== % Shortcuts to blackboard bold. %----------------------------- \newcommand*{\bbA}{\mathbb{A}} \newcommand*{\bbB}{\mathbb{B}} \newcommand*{\bbC}{\mathbb{C}} \newcommand*{\bbD}{\mathbb{D}} \newcommand*{\bbE}{\mathbb{E}} \newcommand*{\bbF}{\mathbb{F}} \newcommand*{\bbG}{\mathbb{G}} \newcommand*{\bbH}{\mathbb{H}} \newcommand*{\bbI}{\mathbb{I}} \newcommand*{\bbJ}{\mathbb{J}} \newcommand*{\bbK}{\mathbb{K}} \newcommand*{\bbL}{\mathbb{L}} \newcommand*{\bbM}{\mathbb{M}} \newcommand*{\bbN}{\mathbb{N}} \newcommand*{\bbO}{\mathbb{O}} \newcommand*{\bbP}{\mathbb{P}} \newcommand*{\bbQ}{\mathbb{Q}} \newcommand*{\bbR}{\mathbb{R}} \newcommand*{\bbS}{\mathbb{S}} \newcommand*{\bbT}{\mathbb{T}} \newcommand*{\bbU}{\mathbb{U}} \newcommand*{\bbV}{\mathbb{V}} \newcommand*{\bbW}{\mathbb{W}} \newcommand*{\bbX}{\mathbb{X}} \newcommand*{\bbY}{\mathbb{Y}} \newcommand*{\bbZ}{\mathbb{Z}} % Shortcuts to script fonts %----------------------------- \newcommand*{\scA}{\mathscr{A}} \newcommand*{\scB}{\mathscr{B}} \newcommand*{\scC}{\mathscr{C}} \newcommand*{\scD}{\mathscr{D}} \newcommand*{\scE}{\mathscr{E}} \newcommand*{\scF}{\mathscr{F}} \newcommand*{\scG}{\mathscr{G}} \newcommand*{\scH}{\mathscr{H}} \newcommand*{\scI}{\mathscr{I}} \newcommand*{\scJ}{\mathscr{J}} \newcommand*{\scK}{\mathscr{K}} \newcommand*{\scL}{\mathscr{L}} \newcommand*{\scM}{\mathscr{M}} \newcommand*{\scN}{\mathscr{N}} \newcommand*{\scO}{\mathscr{O}} \newcommand*{\scP}{\mathscr{P}} \newcommand*{\scQ}{\mathscr{Q}} \newcommand*{\scR}{\mathscr{R}} \newcommand*{\scS}{\mathscr{S}} \newcommand*{\scT}{\mathscr{T}} \newcommand*{\scU}{\mathscr{U}} \newcommand*{\scV}{\mathscr{V}} \newcommand*{\scW}{\mathscr{W}} \newcommand*{\scX}{\mathscr{X}} \newcommand*{\scY}{\mathscr{Y}} \newcommand*{\scZ}{\mathscr{Z}} % Shortcuts to caligraphic %----------------------------- \newcommand*{\caA}{\mathcal{A}} \newcommand*{\caB}{\mathcal{B}} \newcommand*{\caC}{\mathcal{C}} \newcommand*{\caD}{\mathcal{D}} \newcommand*{\caE}{\mathcal{E}} \newcommand*{\caF}{\mathcal{F}} \newcommand*{\caG}{\mathcal{G}} \newcommand*{\caH}{\mathcal{H}} \newcommand*{\caI}{\mathcal{I}} \newcommand*{\caJ}{\mathcal{J}} \newcommand*{\caK}{\mathcal{K}} \newcommand*{\caL}{\mathcal{L}} \newcommand*{\caM}{\mathcal{M}} \newcommand*{\caN}{\mathcal{N}} \newcommand*{\caO}{\mathcal{O}} \newcommand*{\caP}{\mathcal{P}} \newcommand*{\caQ}{\mathcal{Q}} \newcommand*{\caR}{\mathcal{R}} \newcommand*{\caS}{\mathcal{S}} \newcommand*{\caT}{\mathcal{T}} \newcommand*{\caU}{\mathcal{U}} \newcommand*{\caV}{\mathcal{V}} \newcommand*{\caW}{\mathcal{W}} \newcommand*{\caX}{\mathcal{X}} \newcommand*{\caY}{\mathcal{Y}} \newcommand*{\caZ}{\mathcal{Z}} % Shortcuts to bold fonts %----------------------------- \newcommand*{\bfA}{\mathbf{A}} \newcommand*{\bfB}{\mathbf{B}} \newcommand*{\bfC}{\mathbf{C}} \newcommand*{\bfD}{\mathbf{D}} \newcommand*{\bfE}{\mathbf{E}} \newcommand*{\bfF}{\mathbf{F}} \newcommand*{\bfG}{\mathbf{G}} \newcommand*{\bfH}{\mathbf{H}} \newcommand*{\bfI}{\mathbf{I}} \newcommand*{\bfJ}{\mathbf{J}} \newcommand*{\bfK}{\mathbf{K}} \newcommand*{\bfL}{\mathbf{L}} \newcommand*{\bfM}{\mathbf{M}} \newcommand*{\bfN}{\mathbf{N}} \newcommand*{\bfO}{\mathbf{O}} \newcommand*{\bfP}{\mathbf{P}} \newcommand*{\bfQ}{\mathbf{Q}} \newcommand*{\bfR}{\mathbf{R}} \newcommand*{\bfS}{\mathbf{S}} \newcommand*{\bfT}{\mathbf{T}} \newcommand*{\bfU}{\mathbf{U}} \newcommand*{\bfV}{\mathbf{V}} \newcommand*{\bfW}{\mathbf{W}} \newcommand*{\bfX}{\mathbf{X}} \newcommand*{\bfY}{\mathbf{Y}} \newcommand*{\bfZ}{\mathbf{Z}} % Shortcuts to Roman fonts %----------------------------- \newcommand*{\rmA}{\mathrm{A}} \newcommand*{\rmB}{\mathrm{B}} \newcommand*{\rmC}{\mathrm{C}} \newcommand*{\rmD}{\mathrm{D}} \newcommand*{\rmE}{\mathrm{E}} \newcommand*{\rmF}{\mathrm{F}} \newcommand*{\rmG}{\mathrm{G}} \newcommand*{\rmH}{\mathrm{H}} \newcommand*{\rmI}{\mathrm{I}} \newcommand*{\rmJ}{\mathrm{J}} \newcommand*{\rmK}{\mathrm{K}} \newcommand*{\rmL}{\mathrm{L}} \newcommand*{\rmM}{\mathrm{M}} \newcommand*{\rmN}{\mathrm{N}} \newcommand*{\rmO}{\mathrm{O}} \newcommand*{\rmP}{\mathrm{P}} \newcommand*{\rmQ}{\mathrm{Q}} \newcommand*{\rmR}{\mathrm{R}} \newcommand*{\rmS}{\mathrm{S}} \newcommand*{\rmT}{\mathrm{T}} \newcommand*{\rmU}{\mathrm{U}} \newcommand*{\rmV}{\mathrm{V}} \newcommand*{\rmW}{\mathrm{W}} \newcommand*{\rmX}{\mathrm{X}} \newcommand*{\rmY}{\mathrm{Y}} \newcommand*{\rmZ}{\mathrm{Z}} % Shortcuts Fraktur %----------------------------- \newcommand*{\fka}{\mathfrak{a}} \newcommand*{\fkb}{\mathfrak{b}} \newcommand*{\fkc}{\mathfrak{c}} \newcommand*{\fkd}{\mathfrak{d}} \newcommand*{\fke}{\mathfrak{e}} \newcommand*{\fkf}{\mathfrak{f}} \newcommand*{\fkg}{\mathfrak{g}} \newcommand*{\fkh}{\mathfrak{h}} \newcommand*{\fki}{\mathfrak{i}} \newcommand*{\fkj}{\mathfrak{j}} \newcommand*{\fkk}{\mathfrak{k}} \newcommand*{\fkl}{\mathfrak{l}} \newcommand*{\fkm}{\mathfrak{m}} \newcommand*{\fkn}{\mathfrak{n}} \newcommand*{\fko}{\mathfrak{o}} \newcommand*{\fkp}{\mathfrak{p}} \newcommand*{\fkq}{\mathfrak{q}} \newcommand*{\fkr}{\mathfrak{r}} \newcommand*{\fks}{\mathfrak{s}} \newcommand*{\fkt}{\mathfrak{t}} \newcommand*{\fku}{\mathfrak{u}} \newcommand*{\fkv}{\mathfrak{v}} \newcommand*{\fkw}{\mathfrak{w}} \newcommand*{\fkx}{\mathfrak{x}} \newcommand*{\fky}{\mathfrak{y}} \newcommand*{\fkz}{\mathfrak{z}} \newcommand*{\fkA}{\mathfrak{A}} \newcommand*{\fkB}{\mathfrak{B}} \newcommand*{\fkC}{\mathfrak{C}} \newcommand*{\fkD}{\mathfrak{D}} \newcommand*{\fkE}{\mathfrak{E}} \newcommand*{\fkF}{\mathfrak{F}} \newcommand*{\fkG}{\mathfrak{G}} \newcommand*{\fkH}{\mathfrak{H}} \newcommand*{\fkI}{\mathfrak{I}} \newcommand*{\fkJ}{\mathfrak{J}} \newcommand*{\fkK}{\mathfrak{K}} \newcommand*{\fkL}{\mathfrak{L}} \newcommand*{\fkM}{\mathfrak{M}} \newcommand*{\fkN}{\mathfrak{N}} \newcommand*{\fkO}{\mathfrak{O}} \newcommand*{\fkP}{\mathfrak{P}} \newcommand*{\fkQ}{\mathfrak{Q}} \newcommand*{\fkR}{\mathfrak{R}} \newcommand*{\fkS}{\mathfrak{S}} \newcommand*{\fkT}{\mathfrak{T}} \newcommand*{\fkU}{\mathfrak{U}} \newcommand*{\fkV}{\mathfrak{V}} \newcommand*{\fkW}{\mathfrak{W}} \newcommand*{\fkX}{\mathfrak{X}} \newcommand*{\fkY}{\mathfrak{Y}} \newcommand*{\fkZ}{\mathfrak{Z}} % Shortcuts for font types in math mode. %----------------------------- \newcommand*{\mbb}[1]{\mathbb{#1}} % Blackboard Bold \newcommand*{\msf}[1]{\mathsf{#1}} % Serif \newcommand*{\mbf}[1]{\mathbf{#1}} % Bold \newcommand*{\mrm}[1]{\mathrm{#1}} % Roman \newcommand*{\mfk}[1]{\mathfrak{#1}} % Fraktur \newcommand*{\msc}[1]{\mathscr{#1}} % Script \newcommand*{\mca}[1]{\mathcal{#1}} % Calligraphic %% Symbol shortcuts %% ==================================================== % Shortcuts for arrows %----------------------------- \newcommand*{\into}{\hookrightarrow} \newcommand*{\onto}{\twoheadrightarrow} \newcommand*{\cof}{\rightarrowtail} \newcommand*{\fib}{\twoheadrightarrow} \newcommand*{\acof}{\stackrel{\sim}{\rightarrowtail}} \newcommand*{\afib}{\stackrel{\sim}{\twoheadrightarrow}} \newcommand*{\weq}{\stackrel{\sim}{\to}} \newcommand*{\iso}{\stackrel{\simeq}{\to}} %\newcommand*{\rto}{\mathop{\dashrightarrow\!\!\!\!\!% % {\color{white}\blacktriangleright}% % \!\!\!\!\!\!\rightarrow}} \newcommand*{\dashto}{\dashrightarrow} % Brackets %----------------------------- \newcommand{\abs}[1]{\left \lvert #1 \right \rvert} \newcommand{\set}[1]{\left \lbrace #1\right \rbrace} \newcommand{\nrm}[1]{\left \lVert #1 \right \rVert} \newcommand{\abk}[1]{\left \langle #1 \right \rangle} \newcommand{\rbk}[1]{\left ( #1 \right )} \newcommand{\cbk}[1]{\left \lbrace #1 \right \rbrace} \newcommand{\sbk}[1]{\left \lbrack #1 \right \rbrack} \newcommand{\dsbk}[1]{\left \llbracket #1 \right \rrbracket} \newcommand{\bra}[1]{\langle #1 \rvert} \newcommand{\ket}[1]{\lvert #1 \rangle} \newcommand{\qmbk}[2]{\langle #1 \mid #2 \rangle} % Operators %----------------------------- \newcommand*{\tsr}{\otimes} \newcommand*{\btsr}{\boxtimes} \newcommand*{\bigtsr}{\bigotimes} \newcommand*{\tms}{\times} \newcommand*{\rtm}{\rtimes} \newcommand*{\ltm}{\ltimes} \newcommand*{\cuppr}{\smallsmile} \newcommand*{\cappr}{\smallfrown} % Modifiers %----------------------------- \newcommand*{\sla}[1]{\slashed{#1}} \newcommand*{\ol}[1]{\overline{#1}} \newcommand*{\wh}[1]{\widehat{#1}} \newcommand*{\wt}[1]{\widetilde{#1}} % Symbols %----------------------------- \newcommand*{\id}{\mathrm{id}} \newcommand*{\es}{\varnothing} \newcommand*{\sm}{\smallsetminus} \newcommand*{\sub}{\subset} \newcommand*{\subeq}{\subseteq} \newcommand*{\ieq}{\cong} \newcommand*{\deq}{\stackrel{\mathrm{def}}{=}} \newcommand*{\heq}{\simeq} \newcommand*{\dg}{\dagger} \newcommand*{\bt}{\bullet} \newcommand*{\trans}{\pitchfork} \newcommand*{\oo}{\infty} \newcommand*{\cl}{\colon} \newcommand*{\hy}{\text{-}} \newcommand*{\cm}{\circ} \let\amp\& % Operators %----------------------------- \newcommand*{\sq}{\square} \newcommand*{\sqb}{\overline{\square}} \newcommand*{\nbl}{\nabla} \newcommand*{\nblb}{\overline{\nabla}} \newcommand*{\nbls}{\slashed{\nabla}} \newcommand*{\del}{\partial} \newcommand*{\delb}{\overline{\partial}} \newcommand*{\dels}{\slashed{\partial}} \newcommand*{\df}{\mathrm{d}} % Unicode symbols %----------------------------- \ifLuaTeX \newcommand{\acts}{\ensuremath{\,\rotatebox[origin=c]{-90}{$↻$}\,}} \else \newcommand{\acts}{% \ensuremath{\,\rotatebox[origin=c]{-90}{$\raisebox{0.3mm}{\circlearrowright}$}\,} } \fi %% Subject specific symbols %% ==================================================== % Limits and colimits %----------------------------- \DeclareMathOperator{\hocofib}{\mathrm{hocofib}} \DeclareMathOperator{\hofib}{\mathrm{hofib}} \DeclareMathOperator*{\hocolim}{\mathrm{hocolim}} \DeclareMathOperator*{\holim}{\mathrm{holim}} \DeclareMathOperator*{\colim}{\mathrm{colim}} \DeclareMathOperator{\image}{\mathrm{Im}} \DeclareMathOperator{\coker}{\mathrm{coker}} \newcommand*{\plim}{\varprojlim} \newcommand*{\ilim}{\varinjlim} % Hom-sets %----------------------------- \DeclareMathOperator{\Aut}{\mathrm{Aut}} \DeclareMathOperator{\cAut}{\mathcal{A}\mathit{ut}} \DeclareMathOperator{\sAut}{\mathscr{A}\negthinspace\mathit{ut}} \DeclareMathOperator{\bAut}{\mathbf{Aut}} \DeclareMathOperator{\uAut}{\underline{\mathrm{Aut}}} \DeclareMathOperator{\Iso}{\mathrm{Iso}} \DeclareMathOperator{\cIso}{\mathcal{I}\negthinspace\mathit{so}} \DeclareMathOperator{\sIso}{\mathscr{I}\negthickspace\mathit{so}} \DeclareMathOperator{\bIso}{\mathbf{Iso}} \DeclareMathOperator{\uIso}{\underline{\mathrm{Iso}}} \DeclareMathOperator{\Hom}{\mathrm{Hom}} \DeclareMathOperator{\cHom}{\mathcal{H}\negthinspace\mathit{om}} \DeclareMathOperator{\sHom}{\mathscr{H}\negthickspace\mathit{om}} \DeclareMathOperator{\bHom}{\mathbf{Hom}} \DeclareMathOperator{\uHom}{\underline{\mathrm{Hom}}} \DeclareMathOperator{\Map}{\mathrm{Map}} \DeclareMathOperator{\cMap}{\mathcal{M}\mathit{ap}} \DeclareMathOperator{\sMap}{\mathscr{M}\negthinspace\mathit{ap}} \DeclareMathOperator{\bMap}{\mathbf{Map}} \DeclareMathOperator{\uMap}{\underline{\mathrm{Map}}} \DeclareMathOperator{\Mor}{\mathrm{Mor}} \DeclareMathOperator{\cMor}{\mathcal{M}\mathit{or}} \DeclareMathOperator{\sMor}{\mathscr{M}\negthinspace\mathit{or}} \DeclareMathOperator{\bMor}{\mathbf{Mor}} \DeclareMathOperator{\uMor}{\underline{\mathrm{Mor}}} \DeclareMathOperator{\End}{\mathrm{End}} \DeclareMathOperator{\cEnd}{\mathcal{E}\mathit{nd}} \DeclareMathOperator{\sEnd}{\mathscr{E}\negthinspace\mathit{nd}} \DeclareMathOperator{\bEnd}{\mathbf{End}} \DeclareMathOperator{\uEnd}{\underline{\mathrm{End}}} \DeclareMathOperator{\Func}{\mathrm{Func}} \DeclareMathOperator{\bFunc}{\mathbf{Func}} \DeclareMathOperator{\Nat}{\mathrm{Nat}} \DeclareMathOperator{\bNat}{\mathbf{Nat}} % Algebraic Geometry %----------------------------- % Categories \newcommand*{\ctStack}{\mathbf{Stack}} \newcommand*{\ctdStack}{\mathbf{dStack}} \newcommand*{\ctdSch}{\mathbf{dSch}} \newcommand*{\ctSch}{\mathbf{Sch}} \newcommand*{\ctVar}{\mathbf{Var}} \newcommand*{\ctProj}{\mathbf{Proj}} \newcommand*{\ctqProj}{\mathbf{qProj}} \newcommand*{\ctSm}{\mathbf{Sm}} \newcommand*{\ctSmProj}{\mathbf{SmProj}} \newcommand*{\ctCor}{\mathbf{Cor}} \newcommand*{\ctM}{\mathbf{M}} \newcommand*{\ctMM}{\mathbf{MM}} \newcommand*{\ctCoh}{\mathbf{Coh}} \newcommand*{\ctqCoh}{\mathbf{qCoh}} \newcommand*{\ctConst}{\mathbf{Const}} \newcommand*{\ctHdg}{\mathbf{Hdg}} \newcommand*{\ctMHS}{\mathbf{MHS}} \newcommand*{\ctHdgMod}{\mathbf{HdgMod}} \newcommand*{\ctPerv}{\mathbf{Perv}} \newcommand*{\ctBun}{\mathbf{Bun}} \newcommand*{\ctLoc}{\mathbf{Loc}} \newcommand*{\ctDMod}{\mathcal{D}\hy\mathbf{Mod}} \newcommand*{\ctHrc}{\mathbf{Hrc}} \newcommand*{\ctHypCov}{\mathbf{HypCov}} \newcommand*{\ctCov}{\mathbf{Cov}} % Moduli spaces \newcommand*{\Coh}{\mathrm{Coh}} \newcommand*{\sCoh}{\mathscr{C}\negthinspace\mathit{oh}} \newcommand*{\cCoh}{\mathcal{Coh}} \newcommand*{\bCoh}{\mathbf{Coh}} \newcommand*{\Crys}{\mathrm{Crys}} \newcommand*{\sCrys}{\mathscr{C}\negthinspace\mathit{rys}} \newcommand*{\cCrys}{\mathcal{Crys}} \newcommand*{\bCrys}{\mathbf{Crys}} \newcommand*{\Vect}{\mathrm{Vect}} \newcommand*{\cVect}{\mathcal{Vect}} \newcommand*{\sVect}{\mathscr{V}\negthickspace\mathit{ect}} \newcommand*{\bVect}{\mathbf{Vect}} \newcommand*{\Bun}{\mathrm{Bun}} \newcommand*{\cBun}{\mathcal{Bun}} \newcommand*{\sBun}{\mathscr{B}\negthinspace\mathit{un}} \newcommand*{\bBun}{\mathbf{Bun}} \newcommand*{\Loc}{\mathrm{Loc}} \newcommand*{\cLoc}{\mathcal{Loc}} \newcommand*{\sLoc}{\mathscr{L}\negthinspace\mathit{oc}} \newcommand*{\bLoc}{\mathbf{Loc}} \newcommand*{\Hilb}{\mathrm{Hilb}} \newcommand*{\cHilb}{\mathcal{Hilb}} \newcommand*{\sHilb}{\mathscr{H}\negthinspace\mathit{ilb}} \newcommand*{\bHilb}{\mathbf{Hilb}} \newcommand*{\Quot}{\mathrm{Quot}} \newcommand*{\cQuot}{\mathcal{Quot}} \newcommand*{\sQuot}{\mathscr{Q}\negthinspace\mathit{uot}} \newcommand*{\bQuot}{\mathbf{Quot}} \newcommand*{\Pic}{\mathrm{Pic}} \newcommand*{\cPic}{\mathcal{Pic}} \newcommand*{\sPic}{\mathscr{P}\negthinspace\mathit{ic}} \newcommand*{\bPic}{\mathbf{Pic}} \newcommand*{\Grass}{\mathrm{Grass}} \newcommand*{\cGrass}{\mathcal{Grass}} \newcommand*{\sGrass}{\mathscr{G}\negthinspace\mathit{rass}} \newcommand*{\bGrass}{\mathbf{Grass}} \newcommand*{\Frob}{\mathrm{Frob}} \DeclareMathOperator{\Spec}{\mathrm{Spec}} \DeclareMathOperator{\bSpec}{\mathbf{Spec}} \DeclareMathOperator{\Proj}{\mathrm{Proj}} \DeclareMathOperator{\bProj}{\mathbf{Proj}} \DeclareMathOperator{\Sing}{\mathrm{Sing}} \DeclareMathOperator{\Cl}{\mathrm{Cl}} \DeclareMathOperator{\CaCl}{\mathrm{CaCl}} \DeclareMathOperator{\Div}{\mathrm{Div}} \DeclareMathOperator{\divisor}{\mathrm{div}} % \renewcommand*{\div}{\mathrm{\divisor}} % Hey, sure ?!? \DeclareMathOperator{\Res}{\mathrm{Res}} \DeclareMathOperator{\res}{\mathrm{res}} \DeclareMathOperator{\Bl}{\mathrm{Bl}} \DeclareMathOperator{\CH}{\mathrm{CH}} \DeclareMathOperator{\Lsu}{\slashed{\Sigma}} \DeclareMathOperator{\sh}{\mathrm{sh}} \newcommand*{\nis}{\mathrm{nis}} % Nisnevich \newcommand*{\zar}{\mathrm{zar}} % Zariski \newcommand*{\et}{\mathrm{\acute et}} % Etale \newcommand*{\cdh}{\mathrm{cdh}} % cdh \newcommand*{\fppf}{\mathrm{fppf}} % fppf \newcommand*{\fpqc}{\mathrm{fpqc}} % fpqc \newcommand*{\crys}{\mathrm{crys}} % Crystalline \newcommand*{\an}{\mathrm{an}} % analytic \newcommand*{\red}{\mathrm{red}} % reduced \newcommand*{\sst}{\mathrm{sst}} % simplicial semi-topological \newcommand*{\rat}{\mathrm{rat}} % rational \newcommand*{\num}{\mathrm{num}} % numerical \newcommand*{\alg}{\mathrm{alg}} % algebraic \newcommand*{\dR}{\mathrm{dR}} % de Rham \newcommand*{\hdg}{\mathrm{hdg}} % Hodge \newcommand*{\hol}{\mathrm{hol}} % Holonomic %\newcommand*{\hom}{\mathrm{hom}} % homological % Differential geometry %----------------------------- \newcommand*{\ctKah}{\mathbf{K\ddot{a}h}} \newcommand*{\ctMan}{\mathbf{Man}} \newcommand*{\ctSuMan}{\mathbf{SuMan}} \newcommand*{\ctCpx}{\mathbf{Cpx}} \newcommand*{\ctAlCpx}{\mathbf{AlCpx}} \newcommand*{\ctSymp}{\mathbf{Symp}} \newcommand*{\ctFlatBun}{\mathbf{FlatBun}} \newcommand*{\ctHiggs}{\mathbf{Higgs}} % Topology %----------------------------- \newcommand*{\ctpSh}{\mathbf{pSh}} \newcommand*{\ctSh}{\mathbf{Sh}} \newcommand*{\ctTop}{\mathbf{Top}} \newcommand*{\ctSpc}{\mathbf{Spc}} \newcommand*{\ctSpt}{\mathbf{Spt}} \newcommand*{\ctCW}{\mathbf{CW}} \newcommand*{\ctsSet}{\mathbf{sSet}} \newcommand*{\ctKan}{\mathbf{Kan}} \newcommand*{\ctHo}{\mathbf{Ho}} \DeclareMathOperator{\Cyl}{\mathrm{Cyl}} \DeclareMathOperator{\Cone}{\mathrm{Cone}} \DeclareMathOperator{\ch}{\mathrm{ch}} \DeclareMathOperator{\todd}{\mathrm{todd}} \newcommand*{\sing}{\mathrm{sing}} % Singular % Operads %----------------------------- \newcommand*{\ctOp}{\mathbf{Op}} \newcommand*{\ctdgOp}{\mathbf{dgOp}} \newcommand*{\opEnd}{\mathcal{E}\mathit{nd}} \newcommand*{\opAss}{\mathcal{A}\mathit{ss}} \newcommand*{\opLie}{\mathcal{L}\mathit{ie}} \newcommand*{\opCom}{\mathcal{C}\!\mathit{om}} \newcommand*{\opBV}{\mathcal{BV}} \newcommand*{\opGer}{\mathcal{G}\!\mathit{er}} % Algebra %----------------------------- \newcommand*{\ctArt}{\mathbf{Art}} \newcommand*{\ctVect}{\mathbf{Vect}} \newcommand*{\ctCh}{\mathbf{Ch}} \newcommand*{\ctMod}{\mathbf{Mod}} \newcommand*{\ctAb}{\mathbf{Ab}} \newcommand*{\ctsAb}{\mathbf{sAb}} \newcommand*{\ctGrp}{\mathbf{Grp}} \newcommand*{\ctRng}{\mathbf{Rng}} \newcommand*{\ctComRng}{\mathbf{ComRng}} \newcommand*{\ctAlg}{\mathbf{Alg}} \newcommand*{\ctsAlg}{\mathbf{sAlg}} \newcommand*{\ctdgAlg}{\mathbf{dgAlg}} \newcommand*{\ctAooAlg}{A^{\infty}\hy\mathbf{Alg}} \DeclareMathOperator{\Ext}{\mathrm{Ext}} \DeclareMathOperator{\bExt}{\mathbf{Ext}} \DeclareMathOperator{\sExt}{\mathscr{E}\negthickspace\mathit{xt}} \DeclareMathOperator{\Tor}{\mathrm{Tor}} \DeclareMathOperator{\bTor}{\mathbf{Tor}} \DeclareMathOperator{\sTor}{\mathscr{T}\negthickspace\mathit{or}} \DeclareMathOperator{\D}{\mathbf{D}} \DeclareMathOperator{\Doo}{\mathbf{D_{\infty}}} \DeclareMathOperator{\Gal}{\mathrm{Gal}} \DeclareMathOperator{\Gr}{\mathrm{Gr}} \DeclareMathOperator{\Sym}{\mathrm{Sym}} \DeclareMathOperator{\Alt}{\mathrm{Alt}} \DeclareMathOperator{\cha}{\mathrm{char}} \DeclareMathOperator{\Tot}{\mathrm{Tot}} \newcommand*{\ssmpl}{\mathrm{ss}} % Semi simple % Category Theory %----------------------------- \newcommand*{\ctSet}{\mathbf{Set}} \newcommand*{\ctCat}{\mathbf{Cat}} \newcommand*{\ctGpd}{\mathbf{Gpd}} \newcommand*{\ctooCat}{\infty\hy\mathbf{Cat}} \newcommand*{\ctooGpd}{\infty\hy\mathbf{Gpd}} \newcommand*{\ctdgCat}{\mathbf{dgCat}} \newcommand*{\ctStab}{\mathbf{Stab}} \newcommand*{\ctAooCat}{A^{\infty}\hy\mathbf{Cat}} \newcommand*{\ctArr}{\mathbf{Arr}} \newcommand*{\ctDiag}{\mathbf{Diag}} \newcommand*{\ctcoDiag}{\mathbf{coDiag}} \newcommand*{\ctSpan}{\mathbf{Span}} \newcommand*{\Typ}{\mathrm{Typ}} \newcommand*{\op}{\mathrm{op}} % Opposite category \newcommand*{\ctu}{\mathbf{1}} % Monoidal unit % Analysis %----------------------------- \newcommand\pder[2]{\frac{\partial #1}{\partial #2}} \WithSuffix\newcommand\pder*[2]{\sfrac{\partial #1}{\partial #2}} \newcommand\dder[2]{\frac{\mathrm{d} #1}{\mathrm{d} #2}} \WithSuffix\newcommand\dder*[2]{\sfrac{\mathrm{d} #1}{\mathrm{d} #2}} % Lie Groups and Lie algebras %----------------------------- \newcommand*{\lieSL}{\mathrm{SL}} \newcommand*{\lieGL}{\mathrm{GL}} \newcommand*{\lieSO}{\mathrm{SO}} \newcommand*{\lieO}{\mathrm{O}} \newcommand*{\lieU}{\mathrm{U}} \newcommand*{\lieSU}{\mathrm{SU}} \newcommand*{\lieSp}{\mathrm{Sp}} \newcommand*{\liesl}{\mathfrak{sl}} \newcommand*{\liegl}{\mathfrak{gl}} \newcommand*{\lieso}{\mathfrak{so}} \newcommand*{\lieo}{\mathfrak{o}} \newcommand*{\lieu}{\mathfrak{u}} \newcommand*{\liesu}{\mathfrak{su}} \newcommand*{\liesp}{\mathfrak{sp}} % Shortcuts for sub and superscripts. %\newcommand*{\top}{\mathrm{top}} % topological %\newcommand*{\b}{\mathrm{b}} % bounded % Miscelania %----------------------------- \DeclareMathOperator{\codim}{\mathrm{codim}} \DeclareMathOperator{\rank}{\mathrm{rank}} \DeclareMathOperator{\tr}{\mathrm{tr}} \DeclareMathOperator{\Supp}{\mathrm{Supp}} \DeclareMathOperator{\supp}{\mathrm{supp}}