\setlength{\parindent}{0pt} \setlength{\parskip}{1em} \DeclareMathOperator{\area}{area} \let\char\relax \DeclareMathOperator{\char}{char} \DeclareMathOperator{\ord}{ord} \DeclareMathOperator{\Frac}{Frac} \let\div\relax \DeclareMathOperator{\divinternal}{div} \newcommand\div{\glsref[div_symbol]{\divinternal}} \DeclareMathOperator{\Div}{Div} \DeclareMathOperator{\Gal}{Gal} \let\ratmap\dashrightarrow \newcommand\jinv{\glsref[jinv]{j}} \DeclareMathOperator{\Pic}{Pic} \let\cancel\relax \newcommand\tors[1][]{\glsref[tors_symbol]{[#1]}} \DeclareMathOperator{\End}{End} \newcommand\isogip[1]{\glsref[isogip_symbol]{\langle#1\rangle}} \DeclareMathOperator{\trinternal}{tr} \newcommand\isogtr{\glsref[isogip_symbol]{\trinternal}} \newcommand\Z{\glsref[zetafunction_symbol]{Z}} \newcommand\congto{\htmlstackrel{\cong}{\to}} \newcommand\reduction[1]{\glsref[reduction_symbol]{\tilde{#1}}} \newcommand\reductionns[1]{\glsref[reductionns_symbol]{\tilde{#1}_{\text{ns}}}} \newcommand\invlim[1]{{\displaystyle \lim_{\stackrel[#1]{}{\longleftarrow}}}} \newcommand\cK{\glsref[cK_symbol]{c_K}} \newcommand\nr{{\glsref[nr_symbol]{\text{nr}}}} \DeclareMathOperator{\Cl}{Cl} \DeclareMathOperator{\Maps}{Maps} \newcommand\height{\glsref[pointheight_symbol]{H}} \newcommand\ellH{\glsref[ellh_symbol]{H}} \newcommand\ellh{\glsref[ellh_symbol]{h}} \newcommand\canh{\glsref[canh_symbol]{\hat{h}}} \DeclareMathOperator{\summ}{sum} \newcommand\ephi[1][]{\glsref[ephi_symbol]{e_{#1}}} \newcommand\Hone{\glsref[Hone_symbol]{H^1}} \newcommand\Zone{\glsref[Zone_symbol]{Z^1}} \newcommand\Cone{\glsref[Cone_symbol]{C^1}} \newcommand\Bone{\glsref[Bone_symbol]{B^1}} \DeclareMathOperator{\res}{res} \newcommand\Sha{TS} \newcommand\Selmer[1][\phi]{\glsref[selmer_symbol]{S^{(#1)}}} \newcommand\TS{\glsref[TS_symbol]{TS}} \DeclareMathOperator{\coker}{coker} \DeclareMathOperator{\Reg}{Reg}