4 papers
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…