Degree and the Brauer-Manin obstruction

dc.contributor.author	Creutz B
dc.contributor.author	Viray B
dc.date.accessioned	2018-08-16T20:39:49Z
dc.date.available	2018-08-16T20:39:49Z
dc.date.issued	2017	en
dc.date.updated	2018-05-31T22:14:44Z
dc.description.abstract	Let X be a smooth variety over a number field k embedded as a degree d subvariety of {P}^nk and suppose that X is a counterexample to the Hasse principle explained by the Brauer-Manin obstruction. We consider the question of whether the obstruction is given by the d-primary subgroup of the Brauer group, which would have both theoretic and algorithmic implications. We prove that this question has a positive answer in the case of torsors under abelian varieties, Kummer varieties and (conditional on finiteness of Tate-Shafarevich groups) bielliptic surfaces. In the case of Kummer varieties we show, more specifically, that the obstruction is already given by the 2-primary torsion. We construct a conic bundle over an elliptic curve that shows that, in general, the answer is no.	en
dc.identifier.uri	http://hdl.handle.net/10092/15794
dc.language.iso	en
dc.subject	math.NT	en
dc.subject	math.AG	en
dc.subject	14G05, 11G35, 14F22	en
dc.subject.anzsrc	Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theory	en
dc.subject.anzsrc	Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490402 - Algebraic and differential geometry	en
dc.title	Degree and the Brauer-Manin obstruction	en
dc.type	Journal Article	en

Now showing 1 - 1 of 1