The fibration method over real function fields

Publication available at: https://arxiv.org/abs/1811.06192
Title: The fibration method over real function fields
Authors: Pal, A
Endre, S
Item Type: Working Paper
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-Thélène 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. We also show that the strong vanishing conjecture for n-fold Massey products holds for fields of virtual cohomological dimension at most 1 using a theorem of Haran.
Issue Date: 15-Nov-2018
URI: http://hdl.handle.net/10044/1/66466
Copyright Statement: © 2018 The Author(s)
Open Access location: https://arxiv.org/abs/1811.06192
Appears in Collections:Pure Mathematics
Mathematics



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