Place (Field)

A place $\nu$ of a number Field $k$ is an Isomorphism class of field maps $k$ onto a dense subfield of a nondiscrete locally compact Field $k_\nu$.

In the function field case, let $F$ be a function field of algebraic functions of one variable over a Field $K$. Then by a place in $F$, we mean a subset $p$ of $F$ which is the Ideal of nonunits of some Valuation Ring $O$ over $K$.

References

Chevalley, C. Introduction to the Theory of Algebraic Functions of One Variable. Providence, RI: Amer. Math. Soc., p. 2, 1951.

Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.