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arXiv · 1311.3914

Strong approximation and descent

Ulrich Derenthal·Dasheng Wei
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Abstract

We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t)=N_{K/k}(z): firstly for quartic extensions of number fields K/k and quadratic polynomials P(t) in one variable, and secondly for k=Q, an arbitrary number field K and P(t) a product of linear polynomials over Q in at least two variables. Finally, we illustrate that a certain unboundedness condition at archimedean places is necessary for strong approximation.

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Ulrich Derenthal, Dasheng Wei. 2014-12-12. Strong approximation and descent. https://arxiv.org/abs/1311.3914

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