# The Stacks Project

## Tag 0BIK

Definition 9.20.6. Let $L/K$ be a finite extension of fields. The trace pairing for $L/K$ is the symmetric $K$-bilinear form $$Q_{L/K} : L \times L \longrightarrow K,\quad (\alpha, \beta) \longmapsto \text{Trace}_{L/K}(\alpha\beta)$$

The code snippet corresponding to this tag is a part of the file fields.tex and is located in lines 2408–2416 (see updates for more information).

\begin{definition}
\label{definition-trace-pairing}
Let $L/K$ be a finite extension of fields. The {\it trace pairing}
for $L/K$ is the symmetric $K$-bilinear form
$$Q_{L/K} : L \times L \longrightarrow K,\quad (\alpha, \beta) \longmapsto \text{Trace}_{L/K}(\alpha\beta)$$
\end{definition}

There are no comments yet for this tag.

There is also 1 comment on Section 9.20: Fields.

## Add a comment on tag 0BIK

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the lower-right corner).