51 citations · 352 across the 25 of their papers we have counts for
26 papers
Tight approximation for rationally simply connected varieties
Olivier Benoist, Olivier Wittenberg
We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by al…
The Wu relations in real algebraic geometry
Olivier Benoist, Olivier Wittenberg
We construct and study relations between Chern classes and Galois cohomology classes in the Gal(C/R)-equivariant cohomology of real algebraic varieties with no real points. We give…
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…
Some aspects of rational points and rational curves
Olivier Wittenberg
Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent a…
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…
Intermediate Jacobians and rationality over arbitrary fields
Olivier Benoist, Olivier Wittenberg
We prove that a three-dimensional smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. To do so, we develop a…
The tight approximation property
Olivier Benoist, Olivier Wittenberg
This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the…
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.…
The Clemens-Griffiths method over non-closed fields
Olivier Benoist, Olivier Wittenberg
We use the Clemens-Griffiths method to construct smooth projective threefolds, over any field admitting a separable quadratic extension, that are -unirational and -…
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…
On the integral Hodge conjecture for real varieties, II
Olivier Benoist, Olivier Wittenberg
We establish the real integral Hodge conjecture for 1-cycles on various classes of uniruled threefolds (conic bundles, Fano threefolds with no real point, some del Pezzo fibrations…
On the integral Hodge conjecture for real varieties, I
Olivier Benoist, Olivier Wittenberg
We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 o…
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…
A restriction isomorphism for cycles of relative dimension zero
Moritz Kerz, Hélène Esnault, Olivier Wittenberg
We study the restriction map to the closed fiber of a regular projective scheme over an excellent henselian discrete valuation ring, for a cohomological version of the Chow group o…
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…
Transcendental Brauer-Manin obstruction on a pencil of elliptic curves
Olivier Wittenberg
This note gives an explicit example of transcendental Brauer-Manin obstruction to weak approximation. It has two features which the only previously known example of such obstructio…
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…
On the cycle class map for zero-cycles over local fields
Hélène Esnault, Olivier Wittenberg
We study the Chow group of zero-cycles of smooth projective varieties over local and strictly local fields. We prove in particular the injectivity of the cycle class map to integra…
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…
Index of varieties over Henselian fields and Euler characteristic of coherent sheaves
Hélène Esnault, Marc Levine, Olivier Wittenberg
Let X be a smooth proper variety over the quotient field of a Henselian discrete valuation ring with algebraically closed residue field of characteristic p. We show that for any co…
On abelian birational sections
Hélène Esnault, Olivier Wittenberg
For a smooth and geometrically irreducible variety X over a field k, the quotient of the absolute Galois group G_{k(X)} by the commutator subgroup of G_{\bar k(X)} projects onto G_…
Remarks on cycle classes of sections of the arithmetic fundamental group
Hélène Esnault, Olivier Wittenberg
Given a smooth and separated K(pi,1) variety X over a field k, we associate a "cycle class" in etale cohomology with compact supports to any continuous section of the natural map f…