Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Support Varieties and stable cat3egories for algebraic groups   We develop a theory of supports $M \mapsto V(\mathbb G)_M$ for arbitrary
$\mathbb G$-modules $M$ for a linear algebraic group $\mathbb G$ of exponential
type over a field $k$ of positive characteristic $p > 0$. Our construction is
an refinement and a generalization of an earlier approach by the author. We
extend our support theory to apply to bounded complexes of $\mathbb G$-modules,
$C^\bullet \ \mapsto \ V(\mathbb G)_{C^\bullet}$. We introduce the tensor
triangulated category $StMod(\mathbb G)$, a Verdier quotient of the derived
category $D^b(Mod(\mathbb G))$, and we view $StMod(\mathbb G)$ as the stable
module category of $\mathbb G$-modules. Our support theory is well defined on
$StMod(\mathbb G)$, satisfies the "standard properties" for a theory of
supports, and extends the support theory for the Frobenius kernels $\mathbb
G_{(r)} \ \subset \ \mathbb G$ as considered by Suslin, Bendel, and the author.
We also consider the stable module category of finite dimensional $\mathbb
G$-modules, $stmod(\mathbb G)$.
  As an application of our support theory, we employ our support varieties to
establish the classification of $(r)$-complete, thick tensor ideals of
$stmod(\mathbb G)$ by $\mathbb G$ locally closed subsets of $V(\mathbb G)$ and
the classification of $(r)$-complete, localizing tensor ideals of the stable
module category $StMod(\mathbb G)$ by $\mathbb G$-realizable subsets of
$V(\mathbb G)$.

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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin