Degree Three Unramified Cohomology Groups

Abstract

Let $p$ be an odd prime number. Peyre shows that there is a group $G$ of order $p^{12}$ such that $H_{nr}^3(\mathbf{C}(G),\mathbf{Q}/\mathbf{Z})$ is non-trivial. Using Peyre's method, we are able to prove that the same conclusion is true for some groups of order $p^9$.

References in corpus (1)

• The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group)