Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the Cassels-Tate Pairing for Genus Two Jacobians with Rational
  Two Torsion Points   In this paper, we give an explicit formula as well as a practical algorithm
for computing the Cassels-Tate pairing on $\text{Sel}^{2}(J) \times
\text{Sel}^{2}(J)$ where $J$ is the Jacobian variety of a genus two curve under
the assumption that all points in $J[2]$ are $K$-rational. We also give an
explicit formula for the Obstruction map $\text{Ob}: H^1(G_K, J[2]) \rightarrow
\text{Br}(K)$ under the same assumption. Finally, we include a worked example
demonstrating we can indeed improve the rank bound given by a 2-descent via
computing the Cassels-Tate pairing.

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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph