Explicit Computations of Fundamental Classes

Abstract

We use the techniques of group cohomology to give explicit computations of the local fundamental class. As an application, we discuss how to compute the Tate canonical class for the extension $\mathbb{Q}({\zeta }_{p^{\nu }})/\mathbb{Q}$, where $p^{\nu }$ is an odd prime power.

16 pages. Comments welcome!