The fibration method over real function fields

Pal, Ambrus and Szabó, Endre (2020) The fibration method over real function fields. MATHEMATISCHE ANNALEN, 378 (3-4). pp. 993-1019. ISSN 0025-5831

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Abstract

Let R(C) be the function field of a smooth, irreducible projective curve over R. Let X be a smooth, projective, geometrically irreducible variety equipped with a dominant morphism f onto a smooth projective rational variety with a smooth generic fibre over R(C). Assume that the cohomological obstruction introduced by Colliot-Thelene is the only one to the local-global principle for rational points for the smooth fibres of f over R(C)-valued points. Then we show that the same holds for X, too, by adopting the fibration method similarly to Harpaz-Wittenberg.

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