High Quality Content by WIKIPEDIA articles! In the geometry of complex algebraic curves, a local parameter for a curve C at a smooth point P is just a meromorphic function on C that has a simple zero at P. This concept can be generalized to curves defined over fields other than mathbb{C} (or even schemes), due to the fact that the local ring at a smooth point P of an algebraic curve C (defined over an algebraically closed field) is always a discrete valuation ring. This valuation will endow us with a way to count the order (at the point P) of rational functions (which are natural generalizations for meromorphic functions in the non-complex realm) having a zero or a pole at P.

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