Definition 42.68.31. Let $A$ be a Noetherian local domain of dimension $1$ with residue field $\kappa $. Let $K$ be the fraction field of $A$. We define the *tame symbol* of $A$ to be the map

\[ K^* \times K^* \longrightarrow \kappa ^*, \quad (x, y) \longmapsto d_ A(x, y) \]

where $d_ A(x, y)$ is extended to $K^* \times K^*$ by the multiplicativity of Lemma 42.68.30.

## Comments (0)