A transcendence criterion for complex multiplication on algebraic K3 surfaces

04/12/2016 - 12:15pm
04/12/2016 - 1:10pm
Paula Tretkoff (Texas A&M University)

Motivated by his study of the quaternions, William Clifford invented in 1876 the algebras bearing his name (Clifford Algebras) and published his results two years later. In 1967, Kuga and Satake, in a joint paper, used Clifford algebras to associate a complex polarized torus (abelian variety) to a K3 surface, thereby opening the way for the application of results on abelian varieties to K3 surfaces. In this talk, we show how, in a recent paper, we used the Kuga-Satake construction to give a transcendence criterion for complex multiplication on K3 surfaces which generalizes a famous result due to Th. Schneider on the elliptic modular function. We will cover the essentials of Clifford algebras and the Kuga-Satake construction. No background in transcendental number theory will be assumed.

Millikan 2099, Pomona College