Moduli Spaces of Sheaves on K3 Surfaces and Galois Representations

dc.contributor.advisor	Addington, Nicolas
dc.contributor.author	Frei, Sarah
dc.date.accessioned	2019-09-18T19:25:31Z
dc.date.available	2019-09-18T19:25:31Z
dc.date.issued	2019-09-18
dc.description.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.	en_US
dc.identifier.uri	https://hdl.handle.net/1794/24906
dc.language.iso	en_US
dc.publisher	University of Oregon
dc.rights	All Rights Reserved.
dc.title	Moduli Spaces of Sheaves on K3 Surfaces and Galois Representations
dc.type	Electronic Thesis or Dissertation
thesis.degree.discipline	Department of Mathematics
thesis.degree.grantor	University of Oregon
thesis.degree.level	doctoral
thesis.degree.name	Ph.D.

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