Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Brauer-Manin obstruction for constant curves over global function
  fields   Let $\mathbb{F}$ be a finite field and $C,D$ smooth, geometrically
irreducible proper curves over $\mathbb{F}$ and set $K = \mathbb{F}(D)$. We
consider Brauer-Manin and abelian descent obstructions to the existence of
rational points and to weak approximation for the curve $C \otimes_\mathbb{F}
K$. In particular, we show that Brauer-Manin is the only obstruction to weak
approximation and the Hasse principle in the case that the genus of $D$ is less
than that of $C$. We also show that we can identify the points corresponding to
non-constant maps $D \to C$ using Frobenius descents.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th