Properties[edit]
For any finite extension of fields, the restriction of scalars takes quasiprojective varieties to quasiprojective varieties. The dimension of the resulting variety is multiplied by the degree of the extension.
Under appropriate hypotheses (e.g., flat, proper, finitely presented), any morphism of algebraic spaces yields a restriction of scalars functor that takes algebraic stacks to algebraic stacks, preserving properties such as Artin, Deligne-Mumford, and representability.
Weil restrictions vs. Greenberg transforms[edit]
Restriction of scalars is similar to the Greenberg transform, but does not generalize it, since the ring of Witt vectors on a commutative algebra A is not in general an A-algebra.
The original reference is Section 1.3 of Weil's 1959-1960 Lectures, published as:
Other references: