  We study the behaviour of abelian gauge symmetries in six-dimensional N=(1,0)
theories upon decoupling gravity and investigate abelian flavour symmetries in
the context of 6d N=(1,0) SCFTs. From a supergravity perspective, the anomaly
cancellation mechanism implies that abelian gauge symmetries can only survive
as global symmetries as gravity is decoupled. The flavour symmetries obtained
in this way are shown to be free of ABJ anomalies, and their 't Hooft anomaly
polynomial in the decoupling limit is obtained explicitly. In an F-theory
realisation the decoupling of abelian gauge symmetries implies that a
mathematical object known as the height pairing of a rational section is not
contractible as a curve on the base of an elliptic Calabi-Yau threefold. We
prove this prediction from supergravity by making use of the properties of the
Mordell-Weil group of rational sections. In the second part of this paper we
study the appearance of abelian flavour symmetries in 6d N=(1,0) SCFTs. We
elucidate both the geometric origin of such flavour symmetries in F-theory and
their field theoretic interpretation in terms of suitable linear combinations
of geometrically massive U(1)s. Our general results are illustrated in various
explicit examples.
