Dec. 1, 2022
Local-Global Phenomena in Number Theory
Final colloquium of the fall semester
December 1st; 11am; Manchester 121
Abstract: A local-global principle allows us to deduce “global” information from “local” data. In this talk, we’ll discuss such principles (and their failures) in number theory. Two well-known examples include the Hasse-Minkowski theorem on quadratic forms and the Grunwald-Wang theorem on perfect powers. A rich context for local-global phenomena is found in the theory of elliptic curves. We’ll introduce elliptic curves and their Galois representations, and talk about an elegant local-global principle for torsion that is due to Serre and Katz.