Quadratic forms and local-to-global principles
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Description
When trying to find rational solutions to an algebraic equation, a favorite trick is to first look for local solutions. That is, we seek solutions over the reals and modulo all powers of all primes. Sometimes local solutions exist if and only if a rational solution exists. This is when we say that the local-to-global principle holds. We will illustrate this principle by discussing the problem of representing integers by quadratic forms over the rationals.
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