An example of a Brauer–Manin obstruction to weak approximation at a prime with good reduction

We use recent advances in the local evaluation of Brauer elements to study the role played by odd torsion elements of the Brauer group in the arithmetic of diagonal quartic surfaces over arbitrary number fields. We show that over a local field if the order of the Brauer element is odd and coprime to the residue characteristic then the evaluation map it induces on the local points is constant. Over number fields we give a sufficient condition on the coefficients of the equation, which is mild and easy to check, under which the odd torsion does not obstruct weak approximation. We also note a systematic way to produce K 3 K3 surfaces over Q 2 \mathbb {Q}_2 with good reduction and a non-trivial 2-torsion element of the Brauer group with Swan conductor zero.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

An example of a Brauer–Manin obstruction to weak approximation at a prime with good reduction

Abstract: Following Bright and Newton, we construct an explicit K3 surface over the rational numbers having good reduction at 2, and for which 2 is the only prime at which weak approximation is obstructed.

Cited by 2 publications

References 27 publications

Weak approximation for 0-cycles on a product of elliptic curves

Weak approximation for 0-cycles on a product of elliptic curves

Odd torsion Brauer elements and arithmetic of diagonal quartic surfaces over number fields

Contact Info

Product

Resources

About