Strong approximation for a family of norm varieties
Abstract
We study strong approximation of the equation NL/k(x) = Πi=1n pi(t) where L/k is a finite extension of number fields and pi(t)'s are distinct irreducible polynomials over k. We prove this equation satisfies strong approximation with Brauer-Manin obstruction when L can be imbedded in k[t]/(pi(t)) over k for all 1≤ i≤ n. Under Schinzel's hypothesis, we prove that the same result is true without assuming that L can be imbedded in k[t]/(pi(t)) for all 1≤ i≤ n when L/k is cyclic.
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