Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Point counting and Wilkie's conjecture for non-archimedean Pfaffian and
  Noetherian functions   We consider the problem of counting polynomial curves on analytic or
definable subsets over the field ${\mathbb{C}}(\!(t)\!)$, as a function of the
degree $r$. A result of this type could be expected by analogy with the
classical Pila-Wilkie counting theorem in the archimean situation.
  Some non-archimedean analogs of this type have been developed in the work of
Cluckers-Comte-Loeser for the field ${\mathbb{Q}}_p$, but the situation in
${\mathbb{C}}(\!(t)\!)$ appears to be significantly different. We prove that
the set of polynomial curves of a fixed degree $r$ on the transcendental part
of a subanalytic set over ${\mathbb{C}}(\!(t)\!)$ is automatically finite, but
give examples showing that their number may grow arbitrarily quickly even for
analytic sets. Thus no analog of the Pila-Wilkie theorem can be expected to
hold for general analytic sets. On the other hand we show that if one restricts
to varieties defined by Pfaffian or Noetherian functions, then the number grows
at most polynomially in $r$, thus showing that the analog of Wilkie's
conjecture does hold in this context.

34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics