Wednesday 14 December 2016 h.14:30, Room 2BC30

Frances Odumodu (Padova, Dip. Mat.)

“Extension fields, and classes in the genus of a lattice“

Abstract

In this talk, which will be accessible to a large audience, a first part will be devoted to a basic reminder on extension fields with examples, and a second part to the more specific framework of number fields, i.e. finite degree extensions of rational numbers. Concerning the latter part, the Hasse-Minkowski local-global theorem for quadratic forms fails in general at the integral level, hence there are two levels of classification, the genus (local) and the integral class (global): we shall focus on some results concerning the classes in the genus of a lattice and in particular the trace form.