Stack (category theory)

In algebraic geometry, an algebraic stack is a concept introduced to generalize algebraic varieties and schemes. It was proposed by Michael Artin in the mid-1960s, and further developed in works of Deligne and Mumford.

Examples

• Moduli space of algebraic curves (Deligne-Mumford stack) defined as a universal family of curves of given genus g does not exist as an algebraic variety and provides a good example of stack. For elliptic curves over complex numbers this stack is a geometrical factor of upper-half plane by action of modular group.