Inventiones mathematicae

, Volume 171, Issue 2, pp 257–279 | Cite as

Local-global principles for representations of quadratic forms

  • Jordan S. Ellenberg
  • Akshay VenkateshEmail author


We prove a local-global principle for the problem of representations of quadratic forms by quadratic forms over ℤ, in codimension ≥5. The proof uses the ergodic theory of p-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.


Quadratic Form Spin Group Quadratic Space Open Compact Subgroup Hasse Principle 
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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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