51 citations · 352 across the 25 of their papers we have counts for
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Park City lecture notes: around the inverse Galois problem
Olivier Wittenberg
The inverse Galois problem asks whether any finite group can be realised as the Galois group of a Galois extension of the rationals. This problem and its refinements have stimulate…
Supersolvable descent for rational points
Yonatan Harpaz, Olivier Wittenberg
We construct an analogue of the classical descent theory of Colliot-Thélène and Sansuc in which algebraic tori are replaced with finite supersolvable groups. As an application, we…
Rational points on fibrations with few non-split fibres
Yonatan Harpaz, Dasheng Wei, Olivier Wittenberg
We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its depend…
The Massey vanishing conjecture for number fields
Yonatan Harpaz, Olivier Wittenberg
A conjecture of Mináč and Tân predicts that for any n>2, any prime p and any field k, the Massey product of n Galois cohomology classes in H^1(k,Z/pZ) must vanish if it is defined.…
Number fields with prescribed norms
Christopher Frei, Daniel Loughran, Rachel Newton +2
We study the distribution of extensions of a number field with fixed abelian Galois group , from which a given finite set of elements of are norms. In particular, we sho…
Four-fold Massey products in Galois cohomology
Pierre Guillot, Jan Minac, Adam Topaz +1
In this paper, we develop a new necessary and sufficient condition for the vanishing of 4-Massey products of elements in the mod-2 Galois cohomology of a field. This new descriptio…
Rational points and zero-cycles on rationally connected varieties over number fields
Olivier Wittenberg
We report on progress in the qualitative study of rational points on rationally connected varieties over number fields, also examining integral points, zero-cycles, and non-rationa…
Intersections de deux quadriques et pinceaux de courbes de genre 1
Olivier Wittenberg
This research monograph focuses on the arithmetic, over number fields, of surfaces fibred into curves of genus 1 over the projective line, and of intersections of two quadrics in p…
On the fibration method for zero-cycles and rational points
Yonatan Harpaz, Olivier Wittenberg
Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over number fields were proposed by Colliot-Thélène, Sansuc, Kato and Saito in the 1980's. We p…
The Hardy--Littlewood conjecture and rational points
Yonatan Harpaz, Alexei N. Skorobogatov, Olivier Wittenberg
Schinzel's Hypothesis (H) was used by Colliot-Thélène and Sansuc, and later by Serre, Swinnerton-Dyer and others, to prove that the Brauer-Manin obstruction controls the Hasse prin…
A potential analogue of Schinzel's hypothesis for polynomials with coefficients in Fq[t]
Andreas O. Bender, Olivier Wittenberg
The Schinzel hypothesis essentially claims that finitely many irreducible polynomials in one variable over Z simultaneously assume infinitely many prime values unless there is an o…