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number > number theory > Diophantine geometry > field of definition
geometry > algebraic geometry > algebraic variety > field of definition

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field of definition  

Definición

  • 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.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Field_of_definition)

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