Higher dimensional analogues of Châtelet surfaces

Details Higher dimensional analogues of Châtelet surfaces Higher dimensional analogues of Châtelet surfaces

2011-01-28

arxiv.org/abs/1101.5453v2

Mathematics

Number Theory

LaTeX, 10 pages. To appear in the Bulletin of the London Mathematical Society

Scientific paper

We discuss the geometry and arithmetic of higher-dimensional analogues of Ch\^atelet 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-m^{th} powers of a number field are diophantine. Also, given a global field k such that Char(k) = p or k contains the p^{th} roots of unity, we construct a (p+1)-fold that has no k-points and no \'etale-Brauer obstruction to the Hasse principle.

Affiliated with

Also associated with

No associations

Rating

Higher dimensional analogues of Châtelet surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Higher dimensional analogues of Châtelet surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher dimensional analogues of Châtelet surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-551491