A well-know construction of Kuga and Satake associates to the polarized level 2 Hodge structure on a K3 surface a polarized level 1 Hodge structure giving rise to the corresponding Kuga-Satake (abelian) variety. We show how this enables one to prove, for algebraic K3 surfaces, the analogue of Th. Schneider's result that the elliptic modular function j(t) takes an algebraic value at an algebraic argument t if and only if the lattice Z+Zt admits complex multiplications. The proof hinges on results from transcendental number theory. The talk will include an introduction to the Kuga-Satake construction.
A transcendence criterion for complex multiplication on algebraic K3 surfaces [NOTE DAY/TIME]