Motivic Integral of K3 Surfaces over a Non-Archimedean Field

dc.contributor.advisor	Vologodksy, Vadim	en_US
dc.contributor.author	Stewart, Allen	en_US
dc.date.accessioned	2014-09-29T17:52:14Z
dc.date.available	2014-09-29T17:52:14Z
dc.date.issued	2014-09-29
dc.description.abstract	We prove a formula expressing the motivic integral of a K3 surface over C((t)) with semi-stable reduction in terms of the associated limit mixed Hodge structure. Secondly, for every smooth variety over a complete discrete valuation field we define an analogue of the monodromy pairing, constructed by Grothendieck in the case of Abelian varieties, and prove that our monodromy pairing is a birational invariant of the variety. Finally, we propose a conjectural formula for the motivic integral of maximally degenerate K3 surfaces over an arbitrary complete discrete valuation field and prove this conjecture for Kummer K3 surfaces. This dissertation includes previously published co-authored material.	en_US
dc.identifier.uri	https://hdl.handle.net/1794/18418
dc.language.iso	en_US	en_US
dc.publisher	University of Oregon	en_US
dc.rights	All Rights Reserved.	en_US
dc.title	Motivic Integral of K3 Surfaces over a Non-Archimedean Field	en_US
dc.type	Electronic Thesis or Dissertation	en_US
thesis.degree.discipline	Department of Mathematics	en_US
thesis.degree.grantor	University of Oregon	en_US
thesis.degree.level	doctoral	en_US
thesis.degree.name	Ph.D.	en_US

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