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.
Read more about Field Of Definition: Notation, Definitions For Affine and Projective Varieties, Examples, Scheme-theoretic Definitions, Action of The Absolute Galois Group, Further Reading
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