Moduli Stacks of Polarized K3 Surfaces in Mixed Characteristic

By J. Rizov. 2005

80 citations recorded by the source corpus.

In this note we define moduli functors of (primitively) polarized K3 spaces. We show that they are representable by Deligne-Mumford stacks over Spec(Z). Further, we look at K3 spaces with a level structure. Our main result is that the moduli functors of K3 spaces with a primitive polarization of degree 2d and a level structure are representable by smooth algebraic spaces over open parts of Spec(Z). To do this we use ideas of Grothendieck, Deligne, Mumford, Artin and others. These results are the starting point for the theory of complex multiplication for K3 surfaces and the definition of Kuga-Satake abelian varieties in positive characteristic given in our Ph.D. thesis.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c3091cd3fc5dee4187a8655e21c85df63d28d0ec

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Citations in the corpus

Kuga-Satake abelian varieties of K3 surfaces in mixed characteristic (2010, methodology): “Suppose that K is an admissible subgroup of SOðV2dÞðẐÞ (see [42], Definition 5.”
Lectures on K3 Surfaces (2016, methodology): “In analogy to their result, one has the following result, see [507] and Section 4.”
The Tate conjecture for K3 surfaces over finite fields (2012, background): “We briefly recall basic definitions about spin level structures, see [1, 32, 23] to which we refer for further details.”
The Tate conjecture for K3 surfaces in odd characteristic (2013, background): “These compact opens are called admissible in [45].”