Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An upper bound on the Abbes-Saito filtration for finite flat group
  schemes and applications   Let $\cO_K$ be a complete discrete valuation ring of residue characteristic
$p>0$, and $G$ be a finite flat group scheme over $\cO_K$ of order a power of
$p$. We prove in this paper that the Abbes-Saito filtration of $G$ is bounded
by a simple linear function of the degree of $G$. Assume $\cO_K$ has generic
characteristic 0 and the residue field of $\cO_K$ is perfect. Fargues
constructed the higher level canonical subgroups for a Barsotti-Tate group
$\cG$ over $\cO_K$ which is "not too supersingular". As an application of our
bound, we prove that the canonical subgroup of $\cG$ of level $n\geq 2$
constructed by Fargues appears in the Abbes-Saito filtration of the
$p^n$-torsion subgroup of $\cG$.

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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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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: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: cs