Title: Local-global principle for p-extensions in characteristic p
Abstract: 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 a very explicit form: this is Artin-Schreier(-Witt) theory. In this talk, we shall venture beyond the well-trodden path of abelian extensions.
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 of function fields, via the study of a new phenomenon: the fact that the conductor of the minimal solution to a local embedding problem does not change when only the "unramified part" of the embedding problem is modified.
This is joint work with Fabian Gundlach.