Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a deformation theory of finite dimensional modules over repetitive
  algebras   Let $\Lambda$ be a basic finite dimensional algebra over an algebraically
closed field $\mathbf{k}$, and let $\widehat{\Lambda}$ be the repetitive
algebra of $\Lambda$. In this article, we prove that if $\widehat{V}$ is a left
$\widehat{\Lambda}$-module with finite dimension over $\mathbf{k}$, then
$\widehat{V}$ has a well-defined versal deformation ring
$R(\widehat{\Lambda},\widehat{V})$, which is a local complete Noetherian
commutative $\mathbf{k}$-algebra whose residue field is also isomorphic to
$\mathbf{k}$. We also prove that $R(\widehat{\Lambda},\widehat{V})$ is
universal provided that
$\underline{\mathrm{End}}_{\widehat{\Lambda}}(\widehat{V})=\mathbf{k}$ and that
in this situation, $R(\widehat{\Lambda},\widehat{V})$ is stable after taking
syzygies. We apply the obtained results to finite dimensional modules over the
repetitive algebra of the $2$-Kronecker algebra, which provides an alternative
approach to the deformation theory of objects in the bounded derived category
of coherent sheaves over $\mathbb{P}^1_{\mathbf{k}}$

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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg