2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59918The class in the Brauer group of a quaternion algebra over a field is 2-torsion. We study the following question: Which 2-torsion elements of the Brauer group of a complex function field are representable by quaternion algebras? Using intersection theory to show that a certain cohomology class (on a smooth projective model) is the class of an algebraic cycle, we arrive at an obstruction, defined on a subgroup of the 2-torsion of the Brauer group, to representability by quaternion algebras. For the function fields of some complex threefolds, the obstruction map is computed and found to be nontrivial.9 pages, LaTeXAlgebraic Geometry16K50 (Primary) 14C17, 14F22 (Secondary)text