Let L/K be a finite Galois extension of p-adic fields with group G. It is well-known that OL contains a free OK[G]-submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree p of p-adic fields.
How far is an extension of p-adic fields from having a normal integral basis?
Del Corso I.;Lombardo D.
2022-01-01
Abstract
Let L/K be a finite Galois extension of p-adic fields with group G. It is well-known that OL contains a free OK[G]-submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree p of p-adic fields.File in questo prodotto:
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