Explore: Algebraic Spaces

geometric "spaces" and algebraic "structures" is sometimes clear, sometimes elusive. Clearly, groups are algebraic, while Euclidean spaces are geometric

elliptic curve under the functor from complex algebraic spaces to analytic spaces). In fact this algebraic space quotient is not a scheme, is not complete

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants

an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are

In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent

called the continuous dual space. Dual vector spaces find application in many branches of mathematics that use vector spaces, such as in tensor analysis

In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems

operator algebras are often phrased in algebraic terms, while the techniques used are often highly analytic. Although the study of operator algebras is usually

vector space (called vectors). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures