# Moduli stacks of polarized K3 surfaces in mixed characteristic

Serdica Mathematical Journal (2006)

- Volume: 32, Issue: 2-3, page 131-178
- ISSN: 1310-6600

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topRizov, Jordan. "Moduli stacks of polarized K3 surfaces in mixed characteristic." Serdica Mathematical Journal 32.2-3 (2006): 131-178. <http://eudml.org/doc/281448>.

@article{Rizov2006,

abstract = {2000 Mathematics Subject Classification: 14J28, 14D22.In this note we define moduli stacks 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. [J. Rizov. Moduli of K3 Surfaces and Abelian Variaties. Ph. D. thesis, University of Utrecht, 2005]. thesis.},

author = {Rizov, Jordan},

journal = {Serdica Mathematical Journal},

keywords = {K3 Surfaces; Moduli Spaces; moduli spaces},

language = {eng},

number = {2-3},

pages = {131-178},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Moduli stacks of polarized K3 surfaces in mixed characteristic},

url = {http://eudml.org/doc/281448},

volume = {32},

year = {2006},

}

TY - JOUR

AU - Rizov, Jordan

TI - Moduli stacks of polarized K3 surfaces in mixed characteristic

JO - Serdica Mathematical Journal

PY - 2006

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 32

IS - 2-3

SP - 131

EP - 178

AB - 2000 Mathematics Subject Classification: 14J28, 14D22.In this note we define moduli stacks 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. [J. Rizov. Moduli of K3 Surfaces and Abelian Variaties. Ph. D. thesis, University of Utrecht, 2005]. thesis.

LA - eng

KW - K3 Surfaces; Moduli Spaces; moduli spaces

UR - http://eudml.org/doc/281448

ER -

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