Motivic integral of K3 surfaces over a non-archimedean field |
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Authors: | Allen J Stewart Vadim Vologodsky |
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Institution: | University of Oregon, Department of Mathematics, Eugene, OR, United States |
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Abstract: | We prove a formula expressing the motivic integral (Loeser and Sebag, 2003) 34] 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. |
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Keywords: | MSC: primary 14F42 14C25 secondary 14C22 14F05 |
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