Beringter Raum/Morphismus/Modul/Rückzug/Eigenschaften/Fakt

${\displaystyle {}\varphi ^{*}{\mathcal {O}}_{Y}={\mathcal {O}}_{X}\,.}$

${\displaystyle {}V\subseteq Y}$

${\displaystyle {}i_{V}^{*}({\mathcal {G}})=i_{V}^{-1}({\mathcal {G}})={\mathcal {G}}{|}V\,.}$

${\displaystyle \psi \colon (Y,{\mathcal {O}}_{Y})\longrightarrow (Z,{\mathcal {O}}_{Z})}$

in einen weiteren beringten Raum und einen ${\displaystyle {}{\mathcal {O}}_{Z}}$-Modul ${\displaystyle {}{\mathcal {H}}}$ ist ${\displaystyle {}\varphi ^{*}{\left(\psi ^{*}{\mathcal {H}}\right)}={\left(\psi \circ \varphi \right)}^{*}{\mathcal {H}}}$.

${\displaystyle {}V\subseteq Y}$

${\displaystyle {}{\left(\varphi ^{*}{\mathcal {G}}\right)}{|}_{\varphi ^{-1}(V)}={\left(\varphi ^{*}{\mathcal {G}}\right)}{|}_{V}\,.}$