Personal tools
You are here: Home Publications Abelian birational sections in characteristic 0

Abelian birational sections in characteristic 0

Hélène Esnault and Olivier Wittenberg

Number 6
Author Hélène Esnault
Year 2009

For a smooth and geometrically irreducible variety X over a field k of characteristic 0, the quotient of the absolute Galois group Gk(X) by the commutator subgroup of Gk¯(X) projects onto Gk. We investigate the sections of this projection. We show that such sections correspond to "infinite divisions" of the elementary obstruction of Colliot-Thélène and Sansuc. If k is a number field and the Tate-Shafarevich group of the Picard variety of X is finite, then such sections exist if and only if the elementary obstruction vanishes. For curves this condition also amounts to the existence of divisors of degree 1. Finally we show that the vanishing of the elementary obstruction is not preserved by extensions of scalars.

More information about this publication…

Document Actions
December 2017 »
December
MoTuWeThFrSaSu
123
45678910
11121314151617
18192021222324
25262728293031