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Pré-Publication, Document De Travail Année : 2022

Smooth profinite groups, III: the Smoothness Theorem

Résumé

Let $p$ be a prime. The goal of this article is to prove the Smoothness Theorem 5.1 (Theorem D), which notably asserts that a $(1,\infty)$-cyclotomic pair is $(n,1)$-cyclotomic, for all $n \geq 1$. In the particular case of Galois cohomology, the Smoothness Theorem provides a new proof of the Norm Residue Isomorphism Theorem. Using the formalism of smooth profinite groups, this proof presents it as a consequence of Kummer theory for fields.

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hal-03889035 , version 1 (07-12-2022)

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Charles de Clercq, Mathieu Florence. Smooth profinite groups, III: the Smoothness Theorem. 2022. ⟨hal-03889035⟩
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