On diagonal cubic surfaces.
Andrew Bremner (1988)
Manuscripta mathematica
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Andrew Bremner (1988)
Manuscripta mathematica
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T. D. Browning (2003)
Acta Arithmetica
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Israel Vainsencher, Daniel F. Coray (1986)
Commentarii mathematici Helvetici
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Röschel, Otto (2009)
Beiträge zur Algebra und Geometrie
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Daniel F. Coray (1976)
Compositio Mathematica
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Andreas-Stephan Elsenhans, Jörg Jahnel (2012)
Open Mathematics
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We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over ℚ such that Br(S)/Br(ℚ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.
Zeuthen (1875)
Mathematische Annalen
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Anatoly Libgober (1978)
Mathematische Zeitschrift
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P. C. Craighero, R. Gattazzo (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Jun Ho Lee, Stéphane R. Louboutin (2014)
Acta Arithmetica
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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...
R. Conti (1990)
Annales Polonici Mathematici
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Ulrich Sterz (1990)
Banach Center Publications
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Hari das Bagchi, Manindra Chandra Chaki (1952)
Rendiconti del Seminario Matematico della Università di Padova
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