24 citations · 142 across the 24 of their papers we have counts for
4 papers · 1 filter
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 -…