Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of sheaves of locally closed and exact forms   For any smooth projective variety $X$ of dimension $n$ over an algebraically
closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm
T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf
$B^1_X$ of exact 1-forms is stable. When $X$ is a surface with
$\mu(\Omega^1_X)>0$ and $\Omega^1_X$ is semi-stable, the sheaf $B^2_X$ of exact
2-forms is also stable. Moreover, under the same condition, the sheaf $Z^1_X$
of closed 1-forms is stable when $p>3$, and $Z^1_X$ is semi-stable when $p=3$.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ