Approche logarithmique des noyaux \'etales sauvages des corps de nombres
Jean-Fran\c{c}ois Jaulent (IMB), Alexis Michel (IMB)
TL;DR
This paper investigates the l-part of wild étale kernels in number fields, establishing formulas and theorems that connect logarithmic arithmetic with properties of these kernels.
Contribution
It introduces a logarithmic approach to analyze wild étale kernels, deriving new rank formulas, periodicity, reflection theorems, and triviality criteria.
Findings
Derived rank formulas for wild étale kernels
Established periodicity and reflection theorems
Characterized triviality conditions of kernels
Abstract
We study the l-part of the the wild \'etale kernels WK2i(F) of an arbitary number field F for a given prime l in connection with the logarithmic l-class groups. From the logarithmic arithmetic we deduce rank formulas, periodicity and reflection theorems, triviality characterizations and various consequences.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Analytic Number Theory Research