Moduli Spaces of Sheaves on K3 Surfaces and Galois Representations
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Date
2019-09-18
Authors
Frei, Sarah
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Publisher
University of Oregon
Abstract
We consider two K3 surfaces defined over an arbitrary field, together with a smooth proper moduli space of stable sheaves on each. When the moduli spaces have the same dimension, we prove that if the etale cohomology groups with $\Q_\ell$ coefficients of the two surfaces are isomorphic as Galois representations, then the same is true of the two moduli spaces. In particular, if the field of definition is finite and the K3 surfaces have equal zeta functions, then so do the moduli spaces, even when the moduli spaces are not birational. This generalizes works of Mukai, O'Grady, and Markman, who have studied these moduli spaces of sheaves defined over the complex numbers.