A general algorithm computes Selmer groups for finite Galois modules using permutation-module resolutions and Hecke operators.
Extensions and torsors for finite group schemes
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abstract
We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors under such group schemes and groups of isomorphism classes of these objects.
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An algorithm to compute Selmer groups via resolutions by permutations modules
A general algorithm computes Selmer groups for finite Galois modules using permutation-module resolutions and Hecke operators.