Arithmetic of K3 surfaces -- Matthias Schütt

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This talk is concerned with the modularity of K3 surfaces over
the rational numbers. In analogy to elliptic curves, we will
mainly focus on singular K3 surfaces, such that we can
associate a weight 3 newform to the surface. In view of this,
we will also sketch a general approach to newforms with
rational Fourier coefficients and complex multiplication. As
this will imply their finiteness up to twisting, we will
emphasize the question to which weight 3 newform we can
associate a singular K3 surface.