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roydiptajit
roydiptajit
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Suppose $T$ be a system of polynomials homogenous of degree 2 solvable over $\mathbb{R}$ and $\mathbb{Q}_p$ for all primes $p$. So, can we claim that $T$ is solvable over $\mathbb{Q}$? I think as of now there is no local global principle proven for system of polynomials, but could there be one?

Suppose $T$ be a system of polynomials solvable over $\mathbb{R}$ and $\mathbb{Q}_p$ for all primes $p$. So, can we claim that $T$ is solvable over $\mathbb{Q}$? I think as of now there is no local global principle proven for system of polynomials, but could there be one?

Suppose $T$ be a system of polynomials homogenous of degree 2 solvable over $\mathbb{R}$ and $\mathbb{Q}_p$ for all primes $p$. So, can we claim that $T$ is solvable over $\mathbb{Q}$? I think as of now there is no local global principle proven for system of polynomials, but could there be one?

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roydiptajit
roydiptajit
  • 159
  • 7

Local global principle for a system of polynomial equations

Suppose $T$ be a system of polynomials solvable over $\mathbb{R}$ and $\mathbb{Q}_p$ for all primes $p$. So, can we claim that $T$ is solvable over $\mathbb{Q}$? I think as of now there is no local global principle proven for system of polynomials, but could there be one?