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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2621

Title: Noncommutative curves and noncommutative surfaces
Authors: Stafford, JT
VAN DEN BERGH, Michel
Issue Date: 2001
Publisher: AMER MATHEMATICAL SOC
Citation: BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 38(2). p. 171-216
Abstract: In this survey article we describe some geometric results in the theory of noncommutative rings and, more generally, in the theory of abelian categories. Roughly speaking and by analogy with the commutative situation, the category of graded modules modulo torsion over a noncommutative graded ring of quadratic, respectively cubic, growth should be thought of as the noncommutative analogue of a projective curve, respectively surface. This intuition has led to a remarkable number of nontrivial insights and results in noncommutative algebra. Indeed, the problem of classifying noncommutative curves (and noncommutative graded rings of quadratic growth) can be regarded as settled. Despite the fact that no classification of noncommutative surfaces is in sight, a rich body of nontrivial examples and techniques, including blowing up and down, has been developed.
Notes: Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA. Limburgs Univ Ctr, Dept WNI, B-3590 Diepenbeek, Belgium.Stafford, JT, Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA.
URI: http://hdl.handle.net/1942/2621
ISI #: 000167379000003
ISSN: 0273-0979
Category: A1
Type: Journal Contribution
Validation: ecoom, 2002
Appears in Collections: Research publications

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