51 citations · 352 across the 25 of their papers we have counts for
15 papers · 1 filter
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…
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…
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 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 -…
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…
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…
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 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…
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…
On Albanese torsors and the elementary obstruction
Olivier Wittenberg
We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed in terms of the Albanese 1-mot…