Idealizer rings and noncommutative projective geometry

The rings of noncommutative projective geometry

In the past 15 years a study of “noncommutative projective geometry” has flourished. By using and generalizing techniques of commutative projective geometry, one can study certain noncommutative graded rings and obtain results for which no purely algebraic proof is known. For instance, noncommutative graded domains of quadratic growth, or “noncommutative curves,” have now been classified by geo...

The Geometry of Arithmetic Noncommutative Projective Lines

Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space of the form ProjSK(V ), where V be a k-central two-sided vector space over K of rank two and SK(V ) is the noncommutative symmetric algebra generated by V over K defined by M. Van den Bergh [26]. We study the geometry of these spaces. More precisely, we pr...

On Projective Geometry over Full Matrix Rings

1. K. L. Chung, Fluctuation of sums of independent random variables, Ann. of Math. vol. 51 (1950) pp. 697-706. 2. K. L. Chung and P. Erdos, Probability limit theorems assuming only the first moment. I, Memoirs of the American Mathematical Society, no. 6, pp. 13-19. 3.-, On the lower limit of sums of independent random variables, Ann. of Math. vol. 48 (1947) pp. 1003-1013. 4. K. L. Chung and W. ...

Research Statement: Noncommutative Projective Geometry and Vanishing Theorems

1.1. Dissertation. In the past ten years a study of “noncommutative projective geometry” has flourished. By using and generalizing techniques of commutative projective geometry, one can study certain noncommutative rings and obtain results for which no purely algebraic proof is known. The most basic building block of the theory is the twisted homogeneous coordinate ring. Let X be a projective s...

Noncommutative geometry