Shimura varieties and K3 surfaces

Adrian Vasiu, U of U Abstract We first review the connection between polarized K3-surfaces and one partic-

ular Shimura variety Sh(G, X), with G^{ad} = SO(2, 19). Second we use this to prove an arithmetic global Torelli theorem. Third we get some corollaries, inspired from the well known facts for abelian varieties (like Shafarevich type question, extension properties, connectivity aspects, classification over finite fields, etc.).

We do not assume any familary with Shimura varieties. We do assume some familarity with reductive groups and with Witt rings over perfect fields.