Varilly-Alvarado, A.Viray, B.2017-02-242017-02-242012Varilly-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.https://hdl.handle.net/1911/94009We 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.engArticle 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.Journal articlehttp://dx.doi.org/10.1112/blms/bdr075