An algorithm for computing compatibly Frobenius split subvarieties

Details An algorithm for computing compatibly Frobenius split subvarieties An algorithm for computing compatibly Frobenius split subvarieties

2011-04-11

arxiv.org/abs/1104.1937v3

Mathematics

Commutative Algebra

15 pages, many statements clarified and numerous other substantial improvements to the exposition (thanks to the referees). To

Scientific paper

Let $R$ be a ring of prime characteristic $p$, and let $F^e_* R$ denote $R$ viewed as an $R$-module via the $e$th iterated Frobenius map. Given a surjective map $\phi : F^e_* R \to R$ (for example a Frobenius splitting), we exhibit an algorithm which produces all the $\phi$-compatible ideals. We also explore a variant of this algorithm under the hypothesis that $\phi$ is not necessarily a Frobenius splitting (or even surjective). This algorithm, and the original, have been implemented in Macaulay2.

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