Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isogeny classes of abelian varieties with no principal polarizations   We provide a simple method of constructing isogeny classes of abelian
varieties over certain fields k such that no variety in the isogeny class has a
principal polarization. In particular, given a field k, a Galois extension l of
k of odd prime degree p, and an elliptic curve E over k that has no complex
multiplication over k and that has no k-defined p-isogenies to another elliptic
curve, we construct a simple (p-1)-dimensional abelian variety X over k such
that every polarization of every abelian variety isogenous to X has degree
divisible by p^2. We note that for every odd prime p and every number field k,
there exist l and E as above. We also provide a general framework for
determining which finite group schemes occur as kernels of polarizations of
abelian varieties in a given isogeny class.
  Our construction was inspired by a similar construction of Silverberg and
Zarhin; their construction requires that the base field k have positive
characteristic and that there be a Galois extension of k with a certain
non-abelian Galois group.

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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
1
The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn