In mathematics, restriction of scalars (also known as "Weil restriction") is a functor which, for any finite extension of fields L/k and any algebraic variety X over L, produces another variety ResL/kX, defined over k. It is useful for reducing questions about varieties over large fields to questions about more complicated varieties over smaller fields.
Famous quotes containing the words weil and/or restriction:
“If Germany, thanks to Hitler and his successors, were to enslave the European nations and destroy most of the treasures of their past, future historians would certainly pronounce that she had civilized Europe.”
—Simone Weil (19091943)
“If we can find a principle to guide us in the handling of the child between nine and eighteen months, we can see that we need to allow enough opportunity for handling and investigation of objects to further intellectual development and just enough restriction required for family harmony and for the safety of the child.”
—Selma H. Fraiberg (20th century)