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ag.algebraic geometry – Under what circumstances is the polynomial of diploma $6$ irreducible? retort

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ag.algebraic geometry – Under what circumstances is the polynomial of diploma $6$ irreducible?

Let $ok$ breathe a consummate bailiwick of attribute $p neq 2,3$ such that $omega := sqrt[3]{1} in ok$, the place $omega neq 1$. assume a fully irreducible (not essentially homogenous) quadratic polynomial $Q in ok[s_1, s_2]$ in two variables $s_1, s_2$. Under what circumstances is the polynomial $Q^prime(t_1,t_2) := Q(t_1^3, t_2^3)$ (of diploma $6$) completely irreducible (or not less than irreducible over $ok$) ?

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