“The Hasse-Arf theorem and log monogenic extensions”
Mercoledì 8 Ottobre 2025, ore 14:30 - Aula 7B1 - Takeshi Saito (Università di Tokyo)
Abstract
The Hasse-Arf theorem is a central result in the classical ramification theory. It affirms that the conductor of a cyclic extension is an integer. The integrality can be proved by showing an equality of two invariants of the extension defined using two a priori different filtrations.
If we remove the classical assumption that the residue field extension be separable, we have an inequality in general. The equality holds if and only if the extension is log monogenic. Log monogenic extensions are an optimal class of extensions to which classical theorems of ramification theory are extended. They include those with separable residue field extensions.
