\(\require{xypic}\require{newpxtext}\require{newpxmath}\require{cancel}\require{mathrsfs}\require{mathtools}\require{pgfplots} \newenvironment{smallermatrix}[1] {\arraycolsep=0.5pt\def\arraystretch{0.5}\small \array{#1}} {\endarray} \def\coloneqq{\mathrel{\mathop:}\mathrel{\mkern-1.2mu}=} \def\eqqcolon{=\mathrel{\mkern-1.2mu}\mathrel{\mathop:}} \DeclarePairedDelimiter\ceil{\lceil}{\rceil} \DeclarePairedDelimiter\floor{\lfloor}{\rfloor} \newcommand{\ideal}[1]{\mathfrak{#1}} \newcommand{\lie}[1]{\operatorname{\mathfrak{#1}}} \newcommand{\sheaf}[1]{\operatorname{\mathcal{#1}}} \DeclareMathOperator{\Lie}{Lie} \newcommand{\diff}{\mathop{}\!\mathrm{d}} \newcommand{\cinf}{C^\infty} \newcommand{\inv}{^{-1}} \newcommand{\units}{^{\times}} \newcommand{\legendre}[2]{\left(\frac{#1}{#2}\right)} \newcommand{\pair}[2]{\left\langle #1, #2 \right\rangle} \newcommand{\lb}{[} \newcommand{\rb}{]} \newcommand{\powerseries}[2]{#1[[#2]]} \newcommand{\partder}[2][]{\frac{\partial #1}{\partial #2}} \providecommand\mapsfrom{\mathrel{\reflectbox{\ensuremath{\mapsto}}}} \DeclareMathOperator{\Sha}{III} \newcommand{\NN}{\mathbf{N}} \newcommand{\ZZ}{\mathbf{Z}} \newcommand{\QQ}{\mathbf{Q}} \newcommand{\RR}{\mathbf{R}} \newcommand{\CC}{\mathbf{C}} \newcommand{\HH}{\mathbf{H}} \newcommand{\FF}{\mathbf{F}} \newcommand{\GG}{\mathbf{G}} \newcommand{\ints}{\mathcal{O}} \newcommand{\adeles}{\mathbf{A}} \newcommand{\alg}{\mathrm{alg}} \newcommand{\subgroup}{\mathrel{\subseteq}} \newcommand{\cat}[1]{\mathcal{#1}} \newcommand{\catname}[1]{{\mathrm{\textbf{#1}}}} \newcommand{\Rings}{\mathrm{Rings}} \newcommand{\Ar}{\mathrm{Ar}} \newcommand{\dR}{\mathrm{dR}} \newcommand{\crys}{\mathrm{crys}} \newcommand{\cris}{\mathrm{cris}} \newcommand{\et}{\mathrm{\acute{e}t}} \newcommand{\rig}{\mathrm{rig}} \newcommand{\sing}{\mathrm{sing}} \newcommand{\Pet}{\mathrm{Pet}} \newcommand{\pinf}{{1/p^\infty}} \newcommand{\colim}{\operatornamewithlimits{\underset{\longrightarrow}{colim}}} \newcommand{\acts}{\circlearrowright} \newcommand\rightrightrightarrows{ \mathrel{\substack{\textstyle\rightarrow\\[-0.6ex] \textstyle\rightarrow \\[-0.6ex] \textstyle\rightarrow}} } \newcommand{\ab}{\mathrm{ab}} \newcommand{\alm}{\mathrm{a}} \newcommand{\an}{\mathrm{an}} \newcommand{\alt}{\mathrm{alt}} \newcommand{\cyc}{\mathrm{cyc}} \newcommand{\divisible}{\mathrm{div}} \newcommand{\id}{\mathrm{id}} \newcommand{\un}{\mathrm{un}} \newcommand{\nr}{\mathrm{nr}} \newcommand{\ur}{\mathrm{ur}} \newcommand{\tamer}{\mathrm{tr}} \newcommand{\ns}{\mathrm{ns}} \newcommand{\op}{\mathrm{op}} \newcommand{\pre}{\mathrm{pre}} \newcommand{\reg}{\mathrm{reg}} \newcommand{\spec}{\mathrm{spec}} \newcommand{\Set}{\mathrm{Set}} \newcommand{\sep}{\mathrm{sep}} \newcommand{\St}{\mathrm{St}} \newcommand{\tors}{\mathrm{tors}} \newcommand{\transpose}{\mathrm{T}} \newcommand{\semis}{\mathrm{ss}} \DeclareMathOperator{\Ann}{Ann} \DeclareMathOperator{\Ass}{Ass} \DeclareMathOperator{\Supp}{Supp} \DeclareMathOperator{\coker}{coker} \DeclareMathOperator{\lcm}{lcm} \DeclareMathOperator{\End}{End} \DeclareMathOperator{\Diff}{Diff} \DeclareMathOperator{\Hom}{Hom} \newcommand{\sheafHom}{\mathscr{Hom}} \DeclareMathOperator{\Nat}{Nat} \DeclareMathOperator{\Br}{Br} \DeclareMathOperator{\Syl}{Syl} \DeclareMathOperator{\Tgt}{Tgt} \DeclareMathOperator{\sprep}{sp} \DeclareMathOperator{\vol}{Vol} \DeclareMathOperator{\divisor}{div} \DeclareMathOperator{\divisors}{Div} \DeclareMathOperator{\Div}{Div} \DeclareMathOperator{\Cl}{Cl} \DeclareMathOperator{\Pic}{Pic} \DeclareMathOperator{\Jac}{Jac} \DeclareMathOperator{\Princ}{Princ} \DeclareMathOperator{\Cycles}{Cycles} \DeclareMathOperator{\supp}{supp} \DeclareMathOperator{\Ext}{Ext} \DeclareMathOperator{\Tor}{Tor} \DeclareMathOperator{\gr}{gr} \DeclareMathOperator{\Fil}{Fil} \DeclareMathOperator{\polylog}{\mathcal{L}} \DeclareMathOperator{\disc}{disc} \DeclareMathOperator{\Tan}{Tan} \DeclareMathOperator{\Cotan}{Cotan} \DeclareMathOperator{\Sing}{Sing} \DeclareMathOperator{\Sel}{Sel} \DeclareMathOperator{\redu}{red} \DeclareMathOperator{\Reg}{Reg} \DeclareMathOperator{\Rep}{Rep} \DeclareMathOperator{\rk}{rk} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\im}{im} \DeclareMathOperator{\coim}{coim} \DeclareMathOperator{\codim}{codim} \DeclareMathOperator{\Span}{span} \DeclareMathOperator{\characteristic}{char} \DeclareMathOperator{\orient}{or} \DeclareMathOperator{\leadterm}{lt} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\Stab}{Stab} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\ord}{ord} \DeclareMathOperator{\ad}{ad} \DeclareMathOperator{\Ad}{Ad} \DeclareMathOperator{\Spec}{Spec} \DeclareMathOperator{\Proj}{Proj} \DeclareMathOperator{\Spf}{Spf} \DeclareMathOperator{\Spv}{Spv} \DeclareMathOperator{\Spa}{Spa} \DeclareMathOperator{\Spm}{Spm} \DeclareMathOperator{\specialisation}{sp} \DeclareMathOperator{\Max}{Max} \newcommand{\Gal}[2]{\operatorname{Gal}(#1/#2)} \newcommand{\absgal}[1]{\operatorname{Gal}(\overline{#1}/#1)} \newcommand{\sepgal}[1]{\operatorname{Gal}(#1^\sep/#1)} \DeclareMathOperator{\Ind}{Ind} \DeclareMathOperator{\Res}{Res} \DeclareMathOperator{\res}{res} \DeclareMathOperator{\power}{\mathcal{P}} \DeclareMathOperator{\aff}{\mathbf{A}} \DeclareMathOperator{\PP}{\mathbf{P}} \DeclareMathOperator{\norm}{Norm} \DeclareMathOperator{\trace}{Tr} \DeclareMathOperator{\Fr}{Fr} \DeclareMathOperator{\Frob}{Frob} \DeclareMathOperator{\NS}{NS} \DeclareMathOperator{\Der}{Der} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\Out}{Out} \DeclareMathOperator{\Inn}{Inn} \DeclareMathOperator{\vf}{\mathcal{V}} \DeclareMathOperator{\krulldim}{krulldim} \DeclareMathOperator{\trdeg}{trdeg} \DeclareMathOperator{\Frac}{Frac} \DeclareMathOperator{\Prob}{Prob} \DeclareMathOperator{\Mat}{Mat} \DeclareMathOperator{\SL}{SL} \DeclareMathOperator{\GL}{GL} \DeclareMathOperator{\PSL}{PSL} \DeclareMathOperator{\PGL}{PGL} \DeclareMathOperator{\specialorthogonal}{SO} \DeclareMathOperator{\Sp}{Sp} \DeclareMathOperator{\USp}{USp} \DeclareMathOperator{\orth}{O} \DeclareMathOperator{\unitary}{U} \DeclareMathOperator{\specialunitary}{SU} \DeclareMathOperator{\Sym}{Sym} \DeclareMathOperator{\Aff}{Aff} \DeclareMathOperator{\ch}{ch} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)