Unramified cohomology and rationality problems
The aim of this paper is to construct unirational function fields \(K\) over an algebraically closed field of characteristic \(0\) such that the unramified cohomology group \(H^ i_{nr}(K,\mu^{\otimes i}_ p)\neq \{0\}\) for \(i=2,3\) or \(4\) and \(p\) a prime number. This implies that the field \(K\) is not stably rational. For this purpose, a sufficient condition for an element to be unramified in \(H^ i(K,\mu^{\otimes i}_ p)\) is given. This condition relies on computations in the exterior algebra of a vector space of finite dimension over the field \(\mathbb{F}_ p\).
scientific article; zbMATH DE number 537297