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field of definition
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.
==Notation==
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 ''k''alg. The symbols Q, R, C, and F''p'' 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 A''n''(''F'').
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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