New examples of noncommutative surfaces
Abstract: We introduce some graded noetherian rings of dimension 3 - or ``noncommutative surfaces'' - which give counterexamples to several open questions. First, the noetherian property for these algebras is not stable under base extension. Second, these rings have unusual homological properties; in particular they satisfy the \chi_1 condition but not \chi_i for i \geq 2. We will define all of these terms, and discuss the implications of these results for the theory of noncommutative projective geometry.