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Failures of weak approximation in families

Published 5 Jun 2015 in math.NT and math.AG | (1506.01817v2)

Abstract: Given a family of varieties $X\to \mathbb{P}n$ over a number field $k$, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for $100\%$ of the fibres which are everywhere locally soluble.

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