Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hasse principle for homogeneous spaces with nilpotent stabilizer (Le
  principe de Hasse pour les espaces homog\`enes \`a stabilisateur fini)   We prove that the Brauer-Manin obstruction is the only obstruction to the
Hasse principle for homogeneous spaces with nilpotent stabilizer. We thus
generalize recent results by Harpaz and Wittenberg on finite "hyper-solvable"
stabilizers. In particular, this result is true for abelian stabilizers without
any hypotheses on the ambient group, which generalizes classic results by
Borovoi on the subject. We prove moreover that these spaces have the real
approximation property.
  On montre que l'obstruction de Brauer-Manin est la seule obstruction au
principe de Hasse pour les espaces homog\`enes \`a stabilisateur nilpotent. On
g\'en\'eralise ainsi les r\'esultats r\'ecents de Harpaz et Wittenberg sur les
stabilisateurs finis "hyper-r\'esolubles". En particulier, ce r\'esultat vaut
pour les espaces homog\`enes \`a stabilisateur ab\'elien sans hypoth\`ese sur
le groupe ambiant, ce qui g\'en\'eralise des r\'esultats d\'ej\`a classiques de
Borovoi sur le sujet. On d\'emontre au passage que ces espaces poss\`edent la
propri\'et\'e d'approximation r\'eelle.

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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph