Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hasse principle and weak approximation for multinorm equations   In this note, we are interested in local-global principles for multinorm
equations of the form $\prod_{i=1}^n N_{L_i /k}(z_i) = a$ where $k$ is a global
field, $L_i/k$ are finite separable field extensions and $a \in k^*$.
  In particular, we prove a result relating weak approximation for this
equation to weak approximation for some classical norm equation $N_{F/k}(w) =
a$ where $F := \bigcap_{i=1}^n L_i$. It provides a proof of a "weak
approximation" analogue of a recent conjecture by Pollio and Rapinchuk about
multinorm principle. We also provide a counterexample to the original
conjecture concerning Hasse principle.

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The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
1
The categories of this paper are: cs