Parametrization and local-global principle for p-extensions in characteristic p

par Béranger Séguin

jeudi 27 nov. 2025, 14:00 → 15:00 Europe/Paris

One of the main themes of number theory is the description of 
extensions of a fixed (local or global) field. For abelian extensions, this is accomplished by class field theory, which has the distinctive property that local and global extensions are tightly connected.
When restricted to abelian p-extensions in characteristic p, this 
theory takes an explicit form: this is Artin-Schreier(-Witt) theory. In this talk, we shall venture beyond the well-trodden path of abelian extensions, and explore non-abelian generalizations of Artin-Schreier theory.

A specific feature of p-extensions in characteristic p is wild 
ramification, which will enable us to formulate a local-global principle 
in the spirit of class field theory for certain non-abelian /p/-extensions.
This principle relies on a new phenomenon: the invariance of the 
conductor of minimal solutions to local embedding problems when 
modifying only the unramified part of the problem.

This work is a joint collaboration with Fabian Gundlach.