Difference between revisions of "Stack"
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| − | ''' | + | '''Stack''' is a concept introduced in [[algebraic geometry]] to generalize [[algebraic varieties]] and [[schemes]]. They were originally proposed by [[David Mumford]] on the compactifications of moduli of curves; such stack is now called a [[Deligne-Mumford stack]]. They were later generalized by [[Michael Artin]] to [[Artin stack]]s, or sometimes also called [[algebraic stack]]s. More generally a ''stack'' is a [[category]] acting like a [[moduli space]] with a ''universal family'' parametrizing a family of mathematical objects such as schemes or [[topological space]]s. |
==External links== | ==External links== | ||
* ''[http://www.ams.org/notices/200304/what-is.pdf What is... a Stack?]'' | * ''[http://www.ams.org/notices/200304/what-is.pdf What is... a Stack?]'' | ||
| − | [[Category: | + | [[Category:Geometry]] |
| + | [[Category:Algebra]] | ||
Latest revision as of 23:51, June 22, 2010
Stack is a concept introduced in algebraic geometry to generalize algebraic varieties and schemes. They were originally proposed by David Mumford on the compactifications of moduli of curves; such stack is now called a Deligne-Mumford stack. They were later generalized by Michael Artin to Artin stacks, or sometimes also called algebraic stacks. More generally a stack is a category acting like a moduli space with a universal family parametrizing a family of mathematical objects such as schemes or topological spaces.