1、It has developed from two sources: algebraic geometry and algebraic member theory.
3、" In mathematics, a topological space with a family of local coordinate systems related to each other by certain classes of coordinate transformations. Manifolds occur in algebraic geometry, differential equations, and classical dynamics. ."
2、Course in Arithmetic by Jean-Pierre Serre reflects this usage, as do such phrases as first order arithmetic or arithmetical algebraic geometry.