7 papers
The Brauer group of a Stein algebra
Olivier Benoist, James Hotchkiss
We investigate the Brauer group of the ring of holomorphic functions on a finite-dimensional Stein space S. We provide a purely topological computation of this gro…
The resultant divisor is negative
Olivier Benoist
Fix two integers . We study the birational geometry of a parameter space for pairs of homogeneous polynomials of degrees and in two variables (in which the highe…
The Pythagoras number of fields of transcendence degree over
Olivier Benoist
We show that any sum of squares in a field of transcendence degree over is a sum of squares, answering a question of Pop and Pfister. We deduce this result fro…
On the field of meromorphic functions on a Stein surface
Olivier Benoist
We prove that fields of meromorphic functions on Stein surfaces have cohomological dimension 2, and solve the period-index problem and Serre's conjecture II for these fields. We ob…
Stein spaces and Stein algebras
Olivier Benoist
We prove that the category of Stein spaces and holomorphic maps is anti-equivalent to the category of Stein algebras and -algebra morphisms. This removes a finite dimen…
On the Artin vanishing theorem for Stein spaces
Olivier Benoist
Artin vanishing theorems for Stein spaces refer to the vanishing of some of their (co)homology groups in degrees higher than the dimension. We obtain new positive and negative resu…
Smoothing low-dimensional algebraic cycles [after Kollár and Voisin]
Olivier Benoist
Let be a smooth projective complex algebraic variety. An old question of Borel and Haefliger asks whether any (possibly singular) algebraic subvariety of is homologically e…