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In mathematics, an algebraic stack in algebraic geometry is a special case of the concept of a stack, which is useful for working on moduli questions.

There are two main classes of stacks, Deligne-Mumford stack s (DM stacks) and Artin stack s. The initial construction requires a category fibered in groupoid s (CFG), and adds two conditions

a requirement for extending diagrams via cartesian square s, and
the ability to "glue" morphisms and objects, similar to the gluing of local affine spaces into schemes.

External link

For a good introduction to algebraic stacks, see the website of William Fulton.

algebraic geometry Category theory

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Topics: Algebraic Stack, Algebraically Closed Field, Algebraic Number...

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