This research demonstrates an algorithm that computes étale Galois covers on smooth projective curves, suggesting efficient applications in cohomology computation.
We present an algorithm which, given a connected smooth projective curve X over an algebraically closed field of characteristic $p>0$ and its Hasse--Witt matrix, as well as a positive integer n, computes all étale Galois covers of X with group Z/pⁿZ. We compute the complexity of this algorithm when X is defined over a finite field, and provide a complete implementation in SageMath, as well as some explicit examples. We then apply this algorithm to the computation of the cohomology complex of a locally constant sheaf of Z/pⁿZ-modules on such a curve.
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Levrat et al. (2025) studied this question.
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