abstract algebraic geometry造句

• The modern geometric treatment now refers to some basic papers of David Mumford, from 1966 to 1967, which reformulated that theory in terms from abstract algebraic geometry valid over general fields.
• Neither is there any hint that the commutative and noncommutative cases are vastly different, that the former has been successfully recast as a subfield of abstract algebraic geometry, and that the latter is related to geometry as well but in a way which is as yet much more mysterious.
• Further developments included : the extension by Spencer of the techniques to other structures of differential geometry; the assimilation of the Kodaira-Spencer theory into the abstract algebraic geometry of Grothendieck, with a consequent substantive clarification of earlier work; and deformation theory of other structures, such as algebras.