Frobenius and non logarithmic ramification

Frobenius et non-ramification logarithmique

Stéphanie Réglade (1)

1 IMB - Institut de Mathématiques de Bordeaux

A $\ell$-extension is said logarithmically unramified if it is locally cyclotomic. The purpose of this article is to explain the construction of the logarithmic Frobenius, which plays the role usually played by the classical Frobenius, but in the context of the logarithmic ramification.The interesting point is that usual and logarithmic Frobenius coincide when usual and logarithmic ramification are the same.

Mots clés: class field theory; $\ell$-adic class field theory; non-logarithmic ramification

Domaines: Théorie des nombres [math.NT]

Stéphanie Réglade. Frobenius and non logarithmic ramification. 2015. ⟨hal-00999768v3⟩