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
Famous quotes containing the words field of, field and/or definition:
“The field of the poor may yield much food, but it is swept away through injustice.”
—Bible: Hebrew, Proverbs 13:23.
“The frequent failure of men to cultivate their capacity for listening has a profound impact on their capacity for parenting, for it is mothers more than fathers who are most likely to still their own voices so they may hear and draw out the voices of their children.”
—Mary Field Belenky (20th century)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)