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Local-global principles for representations of quadratic forms

Jordan Ellenberg·Akshay Venkatesh
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Abstract

We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension $\geq 7$. 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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Jordan Ellenberg, Akshay Venkatesh. 2006-04-11. Local-global principles for representations of quadratic forms. https://doi.org/10.1007/s00222-007-0077-7

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