51 citations · 235 across the 34 of their papers we have counts for
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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…
Hasse principle for generalised Kummer varieties
Yonatan Harpaz, Alexei N. Skorobogatov
The existence of rational points on Kummer varieties associated to 2-coverings of abelian varieties over number fields can sometimes be proved through the variation of the Selmer g…
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…