Algebra Seminar

Owen Biesel, Carleton College

"G-closures and discriminant algebras"

For a nonseparable finite field extension, the usual Galois correspondence between subextensions of the normal closure and subgroups of its automorphism group breaks down. When we replace fields with rings, it becomes even less clear what the "normal closure" and its automorphism group should be.  Building on work by Bhargava and Satriano, we develop a theory of "G-closure'' for finite ring extensions, restoring a partial correspondence between subgroups and subalgebras, and use it to construct a "discriminant algebra" operation answering a question of Deligne.

MC 5403