Tame symbol

Summary

The tame symbol is a Steinberg symbol attached to a discrete valuation on a field, with values in the multiplicative group of the residue field. It induces the boundary map from $K_2$ of the field to $K_1$ of the residue field. Tame symbols at all primes are the main tool in Tate's computation of $K_2(\Q)$. The Legendre symbol modulo an odd prime $p$ can be read off from the tame symbol at $p$.