Strong approximation for a family of norm varieties
arXiv:1803.11003
Abstract
We study strong approximation of the equation N_{L/k}(x) = \prod_{i=1}^n p_i(t) where L/k is a finite extension of number fields and p_i(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]/(p_i(t)) over k for all 1\leq i\leq n. Under Schinzel's hypothesis, we prove that the same result is true without assuming that L can be imbedded in k[t]/(p_i(t)) for all 1\leq i\leq n when L/k is cyclic.
arXiv commentSection 5 has been changed and an error in Theorem 5.4 has been corrected
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