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About: Noncommutative algebraic geometry     Goto   Sponge   NotDistinct   Permalink

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Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them (e.g. by gluing along localizations or taking noncommutative stack quotients). One of the values of the field is that it also provides new techniques to study objects in commutative algebraic geometry such as Brauer groups.