Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a theorem of Faltings on formal functions   In 1980, Faltings proved, by deep local algebra methods, a local result
regarding formal functions which has the following global geometric fact as a
consequence.
  Theorem: Let k be an algebraically closed field (of any characteristic). Let
Y be a closed subvariety of a projective irreducible variety X defined over k.
Assume that X \subseteq P^n, dim(X)=d>2 and Y is the intersection of X with r
hyperplanes of P^n, with r \le d-1. Then, every formal rational function on X
along Y can be (uniquely) extended to a rational function on X.
  Due to its importance, the aim of this paper is to provide two elementary
global geometric proofs of this theorem.

33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org