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arXiv · 2609.37931

The WittVectors package for Macaulay2

Anne Fayolle·Abhay Goel·Devlin Mallory·Eamon Quinlan-Gallego·Teppei Takamatsu
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Abstract

We implement a Macaulay2 package for computations involving rings of truncated Witt vectors $W_n(R)$ of a finitely generated $\F_p$-algebra $R$. This package includes ring operations (addition, multiplication, Frobenius, Verschiebung, etc.) on elements of $W_n(R)$, conversion between tuple representatives and ghost map representatives of elements of truncated Witt vectors over polynomial rings, and explicit computation of $W_n(R)$ as a finite-type algebra over $\Z/p^n$. This functionality is based on an algorithm we developed for performing arithmetic operations in rings of finite length $p$-typical Witt vectors over finitely generated $\F_p$-algebras. In addition, we implement an algorithm to calculate lifts of Frobenius from $\F_p$-algebras to flat lifts over $\Z/p^2\Z$, and an algorithm to find the quasi-$F$-splitting height of a local or graded complete intersection ring.

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Anne Fayolle, Abhay Goel, Devlin Mallory, Eamon Quinlan-Gallego, Teppei Takamatsu. 2026-09-29. The WittVectors package for Macaulay2. https://arxiv.org/abs/2609.37931

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