Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 2 (2019), 321-327.

Failure of strong approximation on an affine cone

Martin Bright and Ivo Kok

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Abstract

We use the Brauer–Manin obstruction to strong approximation on a punctured affine cone to explain why some mod p solutions to a homogeneous Diophantine equation of degree 2 cannot be lifted to coprime integer solutions.

Article information

Source
Involve, Volume 12, Number 2 (2019), 321-327.

Dates
Received: 27 November 2017
Revised: 29 January 2018
Accepted: 13 March 2018
First available in Project Euclid: 25 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.involve/1540432920

Digital Object Identifier
doi:10.2140/involve.2019.12.321

Mathematical Reviews number (MathSciNet)
MR3864220

Zentralblatt MATH identifier
06980504

Subjects
Primary: 11G35: Varieties over global fields [See also 14G25]
Secondary: 14G25: Global ground fields 14F22: Brauer groups of schemes [See also 12G05, 16K50] 11D09: Quadratic and bilinear equations

Keywords
Brauer–Manin obstruction integral points strong approximation

Citation

Bright, Martin; Kok, Ivo. Failure of strong approximation on an affine cone. Involve 12 (2019), no. 2, 321--327. doi:10.2140/involve.2019.12.321. https://projecteuclid.org/euclid.involve/1540432920


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References

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  • R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer, 1977.
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