Local-global principles for representations of quadratic forms
Jordan Ellenberg, Akshay Venkatesh
Abstract
We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension ≥ 7. 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.
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