Motivic integral of K3 surfaces over a non-archimedean field

Details Motivic integral of K3 surfaces over a non-archimedean field Motivic integral of K3 surfaces over a non-archimedean field

2011-01-05

arxiv.org/abs/1101.0874v3

Mathematics

Algebraic Geometry

LATEX, 37 pages. Final version; Advances in Mathematics, Volume 228, Issue 5 (2011)

Scientific paper

We prove a formula expressing the motivic integral (\cite{ls}) of a K3 surface over $\bC((t))$ with semi-stable reduction in terms of the associated limit Hodge structure. Secondly, for every smooth variety over a non-archimedean 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 degenerated K3 surfaces over an arbitrary non-archimedean field and prove this conjecture for Kummer K3 surfaces.

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