frobeniusDirectImage(p, C)
frobeniusDirectImage_p C
The $p$th toric Frobenius is a toric morphism $F_p \colon X \rightarrow X$ which is the extension of the natural group homomorphism $T_X \rightarrow T_X$ given by raising all coordinates to the $p$th power. This allows one to view the Cox ring $R$ of $X$ as a module over itself, with the module action being $r \cdot m :\!= r^p m$. The extension of this action to modules also allows one to compute the pushforward by $F_p$. Note that $p$ need not be prime, nor related to the characteristic of the ground field in any way. The pushforward is an endofunctor on the category of $R$-modules, so we may apply it to complexes of $R$-modules.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/ToricHigherDirectImages.m2:707:0.