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arXiv · 1803.11003

Strong approximation for a family of norm varieties

Yang Cao·Dasheng Wei·Fei Xu
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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.

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Yang Cao, Dasheng Wei, Fei Xu. 2018-03-29. Strong approximation for a family of norm varieties. https://arxiv.org/abs/1803.11003

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