Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge groups of abelian varieties with purely multiplicative reduction   The main result of the paper is that if $A$ is an abelian variety over a
subfield $F$ of ${\bold C}$, and $A$ has purely multiplicative reduction at a
discrete valuation of $F$, then the Hodge group of $A$ is semisimple. Further,
we give necessary and sufficient conditions for the Hodge group to be
semisimple. We obtain bounds on certain torsion subgroups for abelian varieties
which do not have purely multiplicative reduction at a given discrete
valuation, and therefore obtain bounds on torsion for abelian varieties,
defined over number fields, whose Hodge groups are not semisimple.

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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th