Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The support of top graded local cohomology modules   Let $R_0$ be any domain, let $R=R_0[U_1, ..., U_s]/I$, where $U_1, ..., U_s$
are indeterminates of some positive degrees, and $I\subset R_0[U_1, ..., U_s]$
is a homogeneous ideal.
  The main theorem in this paper is states that all the associated primes of
$H:=H^s_{R_+}(R)$ contain a certain non-zero ideal $c(I)$ of $R_0$ called the
``content'' of $I$. It follows that the support of $H$ is simply
$V(\content(I)R + R_+)$ (Corollary 1.8) and, in particular, $H$ vanishes if and
only if $c(I)$ is the unit ideal.
  These results raise the question of whether local cohomology modules have
finitely many minimal associated primes-- this paper provides further evidence
in favour of such a result.
  Finally, we give a very short proof of a weak version of the monomial
conjecture based on these results.

31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom