Insufficiency of the Brauer–Manin Obstruction for Rational Points on Enriques Surfaces

Francesca Balestrieri,Jennifer Berg,Michelle Manes,Jennifer Park,Bianca Viray

doi:10.1007/978-3-319-30976-7_1

Insufficiency of the Brauer–Manin Obstruction for Rational Points on Enriques Surfaces

Francesca Balestrieri, Jennifer Berg + Show 3 more

https://doi.org/10.1007/978-3-319-30976-7_1

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Publication Date: Jan 1, 2016

Citations: 3

Affiliation: University of Oxford, The University of Texas at Austin, University of Hawaiʻi at Mānoa, University of Michigan–Ann Arbor, University of Washington, Seattle University

#Brauer Manin Obstruction #Enriques Surfaces + Show 4 more

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Abstract

In Varilly-Alvarado and Viray (Adv. Math. 226(6):4884–4901, 2011), the authors constructed an Enriques surface X over \(\mathbb{Q}\) with an etale-Brauer obstruction to the Hasse principle and no algebraic Brauer–Manin obstruction. In this paper, we show that the nontrivial Brauer class of \(X_{\overline{\mathbb{Q}}}\) does not descend to \(\mathbb{Q}\). Together with the results of Varilly-Alvarado and Viray (Adv. Math. 226(6):4884–4901, 2011), this proves that the Brauer–Manin obstruction is insufficient to explain all failures of the Hasse principle on Enriques surfaces.

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