Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Motivic integral of K3 surfaces over a non-archimedean field   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.

21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an