The set of nonsquares in a number field is diophantine

DOI10.4310/MRL.2009.v16.n1.a16zbMath1183.14031arXiv0712.1785MaRDI QIDQ1012975

Bjorn Poonen

Publication date: 28 April 2009

Published in: Mathematical Research Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.1785

zbMATH Keywords

Châtelet surfaceBrauer--Manin obstructiondiophantine set

Mathematics Subject Classification ID

Rational points (14G05) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Global ground fields in algebraic geometry (14G25) Connections of number theory and logic (11U99)

Related Items (5)

Defining the integers in large rings of a number field using one universal quantifier ⋮ Le complémentaire des puissances -ièmes dans un corps de nombres est un ensemble diophantien ⋮ Defining \(\mathbb Z\) in \(\mathbb Q\) ⋮ Diophantine definability of nonnorms of cyclic extensions of global fields ⋮ Smooth compactifications of certain normic bundles

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