Higher-dimensional analogs of Chatelet surfaces

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dc.citation.firstpage125en_US
dc.citation.journalTitleBulletin of the London Mathematical Societyen_US
dc.citation.lastpage135en_US
dc.citation.volumeNumber44en_US
dc.contributor.authorVarilly-Alvarado, A.en_US
dc.contributor.authorViray, B.en_US
dc.date.accessioned2017-02-24T19:14:11Z
dc.date.available2017-02-24T19:14:11Z
dc.date.issued2012en_US
dc.description.abstractWe discuss the geometry and arithmetic of higher-dimensional analogs of Chatelet surfaces; namely, we describe the structure of their Brauer and Picard groups and show that they can violate the Hasse principle. In addition, we use these varieties to give straightforward generalizations of two recent results of Poonen. Specifically, we prove that, assuming Schinzel's hypothesis, the non-mth powers of a number field are diophantine. Also, given a global field k such that Char(k)=p or k contains the pth roots of unity, we construct a (p+1)-fold that has no k-points and no etale-Brauer obstruction to the Hasse principle.en_US
dc.identifier.citationVarilly-Alvarado, A. and Viray, B.. "Higher-dimensional analogs of Chatelet surfaces." <i>Bulletin of the London Mathematical Society,</i> 44, (2012) London Mathematical Society: 125-135. http://dx.doi.org/10.1112/blms/bdr075.
dc.identifier.doihttp://dx.doi.org/10.1112/blms/bdr075en_US
dc.identifier.urihttps://hdl.handle.net/1911/94009
dc.language.isoengen_US
dc.publisherLondon Mathematical Society
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.titleHigher-dimensional analogs of Chatelet surfacesen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
local.sword.agentConverisen_US
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