24 citations · 142 across the 24 of their papers we have counts for
24 papers · 1 filter
Separating components of real algebraic varieties by cohomological invariants
Olivier Benoist, Samuel Lerbet
Let be a smooth algebraic variety over . We study the separation of the connected components of by equivariant cohomology, unramified cohomology, an…
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…
On the rationality of some real threefolds
Olivier Benoist, Alena Pirutka
We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which t…
On the smoothability problem with rational coefficients
Olivier Benoist, Claire Voisin
We consider the problem of smoothing algebraic cycles with rational coefficients on smooth projective complex varieties up to homological equivalence. We show that a solution to th…
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…
Étale cohomology of algebraic varieties over Stein compacta
Olivier Benoist
We prove a comparison theorem between the étale cohomology of algebraic varieties over Stein compacta and the singular cohomology of their analytifications. We deduce that the fiel…
Steenrod operations and algebraic classes
Olivier Benoist
Based on a relative Wu theorem in étale cohomology, we study the compatibility of Steenrod operations on Chow groups and on étale cohomology. Using the resulting obstructions to al…
Smooth subvarieties of Jacobians
Olivier Benoist, Olivier Debarre
We give new examples of algebraic integral cohomology classes on smooth projective complex varieties that are not integral linear combinations of classes of smooth subvarieties. So…
On the bad points of positive semidefinite polynomials
Olivier Benoist
A bad point of a positive semidefinite real polynomial f is a point at which a pole appears in all expressions of f as a sum of squares of rational functions. We show that quartic…
On the subvarieties with nonsingular real loci of a real algebraic variety
Olivier Benoist
Let be a smooth projective real algebraic variety. We give new positive and negative results on the problem of approximating a submanifold of the real locus of by real loci…
Two coniveau filtrations
Olivier Benoist, John Christian Ottem
A cohomology class of a smooth complex variety of dimension has coniveau if it vanishes in the complement of a closed subvariety of codimension , and has stron…
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…
Sums of squares in function fields over Henselian local fields
Olivier Benoist
We give upper bounds for the level and the Pythagoras number of function fields over fraction fields of integral Henselian excellent local rings. In particular, we show that the Py…
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 -…
The period-index problem for real surfaces
Olivier Benoist
We study when the period and the index of a class in the Brauer group of the function field of a real algebraic surface coincide. We prove that it is always the case if the surface…
Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero
Olivier Benoist, John Christian Ottem
We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first e…
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…
Sums of three squares and Noether-Lefschetz loci
Olivier Benoist
We show that the set of real polynomials in two variables that are sums of three squares of rational functions is dense in the set of those that are positive semidefinite. We also…
On Hilbert's 17th problem in low degree
Olivier Benoist
Artin solved Hilbert's 17th problem, proving that a real polynomial in variables that is positive semidefinite is a sum of squares of rational functions, and Pfister showed tha…
Complete families of smooth space curves and strong semistability
Olivier Benoist
We construct the first non-trivial examples of complete families of non-degenerate smooth space curves, and show that the base of such a family cannot be a rational curve. Both res…
On the birational geometry of the parameter space for codimension 2 complete intersections
Olivier Benoist
Codimension 2 complete intersections in P^N have a natural parameter space \bar{H}: a projective bundle over a projective space given by the choice of the lower degree equation and…
Quasi-projectivity of normal varieties
Olivier Benoist
We prove that a normal variety contains finitely many maximal quasi-projective open subvarieties. As a corollary, we obtain the following generalization of the Chevalley-Kleiman pr…