Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-invariance of weak approximation properties under extension of the
  ground field   For rational points on algebraic varieties defined over a number field $K$,
we study the behavior of the property of weak approximation with Brauer-Manin
obstruction under extension of the ground field. We construct K-varieties
accompanied with a quadratic extension $L/K$ such that the property holds over
$K$ (conditional on a conjecture) while fails over $L$. The result is
unconditional when $K = \mathbb{Q}$ or $K$ is one of several quadratic number
fields. Over $\mathbb{Q}$, we give an explicit example.

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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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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: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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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: ao-sci