frobeniusDirectImage(p, M)
frobeniusDirectImage_p M
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. Here is the 4th pushforward of the Cox ring of the first Hirzebruch surface.
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We can pushforward many kinds of modules. Here is the pushforward of an ideal.
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Here is the pushforward of a free module.
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Here is the pushforward of a torsion module.
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As mentioned, $p$ is not related to the characteristic of the field, and the outputs will be the same modules over a different coefficient ring.
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The object frobeniusDirectImage is a method function.
The source of this document is in ToricHigherDirectImages.m2:634:0.