Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the zeta function of divisors for projective varieties with higher
  rank divisor class group   Given a projective variety X defined over a finite field, the zeta function
of divisors attempts to count all irreducible, codimension one subvarieties of
X, each measured by their projective degree. When the dimension of X is greater
than one, this is a purely p-adic function, convergent on the open unit disk.
Four conjectures are expected to hold, the first of which is p-adic meromorphic
continuation to all of C_p.
  When the divisor class group (divisors modulo linear equivalence) of X has
rank one, then all four conjectures are known to be true. In this paper, we
discuss the higher rank case. In particular, we prove a p-adic meromorphic
continuation theorem which applies to a large class of varieties. Examples of
such varieties are projective nonsingular surfaces defined over a finite field
(whose effective monoid is finitely generated) and all projective toric
varieties (smooth or singular).

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex