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Noncrossed products over $k_{\mathfrak {p}}(t)$
Noncrossed product division algebras are constructed over rational function fields $k(t)$ over number fields $k$ by lifting from arithmetic completions $k(t)_{\mathfrak {p}}$. The existence of noncrossed products over $\mathfrak {p}$-adic rational function fields $k_{\mathfrak {p}}(t)$ is proved as a corollary.