High Quality Content by WIKIPEDIA articles! In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K, it may not be obvious whether there is a smaller field k, and other polynomials defined over k, which still define V. The issue of field of definition is of concern in diophantine geometry. Throughout this article, k denotes a field. The algebraic closure of a field is denoted by adding a superscript of "alg", e.g. the algebraic closure of k is kalg. The symbols Q, R, C, and Fp represent, respectively, the field of rational numbers, the field of real numbers, the field of complex numbers, and the finite field containing p elements. Affine n-space over a field F is denoted by An(F).

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