  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.

Algebraic Geometry