Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Conjecture of Lan-Sheng-Zuo on Semistable Higgs Bundles: Rank 3
  Case   Let $X$ be a smooth projective curve of genus $g$ over an algebraically
closed field $k$ of characteristic $p>2$. We prove that any rank $3$ nilpotent
semistable Higgs bundle $(E,\theta)$ on $X$ is a strongly semistable Higgs
bundle. This gives a partially affirmative answer to a conjecture of
Lan-Sheng-Zuo \cite{LanShengZuo12ii}\footnotemark[1]. In addition, we prove a
tensor product theorem for strongly semistable Higgs bundles with $p$
satisfying some bounds (Theorem \ref{TensorTheorem}). From this we reprove a
tensor theorem for semistable Higgs bundles on the condition that the
Lan-Sheng-Zuo conjecture holds (Corollary \ref{TensorStableBundle}).

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The categories of this paper are: stat
1
The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th