Discriminants of totally wild extensions

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Mathematics (MSc)

Buise, Matthijs (2026)

Discriminants of totally wild extensions

Master thesis | Mathematics (MSc)

We study totally wild extensions of local fields. To such an extension, we associate a cohomological invariant derived from the discriminant of a generator. Under suitable divisibility conditions, we prove that this invariant attains all possible values. The construction provides a tool for the study of totally wild extensions, which are in general poorly understood. Our proof uses non-standard group-theoretic methods, including a generalization of the transfer homomorphism and a notion of determinants of automorphisms of p-groups. These methods may be of independent interest.