Say we have a polynomial in a cyclotomic field; in particular, an n-th cyclotomic field, where n is the order of the polynomial's symmetry group. If we know the polynomial is smooth over this field, can we extrapolate that the polynomial is smooth over $\mathbb{C}$? Is there any existing theorem that states some variation of this?
2026-03-25 19:25:07.1774466707
Smoothness in cyclotomic versus complex fields?
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