Zeros of pairs of quadratic forms
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D. R. Heath-Brown
Abstract
We prove the Hasse principle and weak approximation for varieties defined over number fields by the nonsingular intersection of pairs of quadratic forms in eight variables. The argument develops work of Colliot-Thélène, Sansuc and Swinnerton-Dyer, and centres on a purely local problem about forms which split off three hyperbolic planes.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Mean curvature self-shrinkers of high genus: Non-compact examples
- Zeros of pairs of quadratic forms
- The Stokes groupoids
- Severi degrees on toric surfaces
- Homology of SL2 over function fields I: Parabolic subcomplexes
- Mean dimension, mean rank, and von Neumann–Lück rank
- Pluriclosed flow on generalized Kähler manifolds with split tangent bundle
- Parabolic curves of diffeomorphisms asymptotic to formal invariant curves
- Xiao’s conjecture for general fibred surfaces
Artikel in diesem Heft
- Frontmatter
- Mean curvature self-shrinkers of high genus: Non-compact examples
- Zeros of pairs of quadratic forms
- The Stokes groupoids
- Severi degrees on toric surfaces
- Homology of SL2 over function fields I: Parabolic subcomplexes
- Mean dimension, mean rank, and von Neumann–Lück rank
- Pluriclosed flow on generalized Kähler manifolds with split tangent bundle
- Parabolic curves of diffeomorphisms asymptotic to formal invariant curves
- Xiao’s conjecture for general fibred surfaces
