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Constructions using Galois Theory

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arxiv 2010.01281 v3 pith:6LMJEBLP submitted 2020-10-03 math.NT

Claus Fieker , Nicole Sutherland This is my paper · ORCID
classification math.NT
keywords galoisdescribefieldfieldsgroupssplittingtowersabsolute
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We describe algorithms to compute fixed fields, splitting fields and towers of radical extensions without using polynomial factorisation in towers or constructing any field containing the splitting field, instead extending Galois group computations for this task. We also describe the computation of geometric Galois groups (monodromy groups) and their use in computing absolute factorizations.

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  1. An algorithm to compute Selmer groups via resolutions by permutations modules

    cs.SC 2025-04 conditional novelty 6.0 of 10

    A general algorithm computes Selmer groups for finite Galois modules using permutation-module resolutions and Hecke operators.

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