S. P. Smith

Learn More
This paper concerns curves on non-commutative schemes, hereafter called quasi-schemes. A quasi-scheme X is identiied with the category ModX of quasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embedded hypersurface Y. Let C be a curve on X which is in \good posi-tion" with respect to Y (see Deenition 5.1)|this deenition includes a(More)
egalement que l'alg ebre de Sklyanin peut ^ etre d eenie a l'aide des bilin eaires s'annulant sur une certaine sous-vari et e de P 3 P 3 : ABSTRACT. This paper studies point modules and line modules over the algebra deened by E.K. Sklyanin in 17]. It was proved in 21] that the point modules are in bijection with the points of an elliptic curve E in P 3(More)
For a 3-dimensional Artin-Schelter-regular algebra A with Hilbert series (1 ? t) ?3 we study central extensions; that is, graded algebras D with a regular central element z in degree 1, such that D=(z) = A. We classify such D and we also classify certain D-modules (point modules and line modules) which proved to be important in the study of 3-dimensional(More)
We study basic properties of Auslander-Gorenstein rings related to duality, localization and purity of minimal injective resolutions. Contents 0. Introduction and deenitions 1. Duality between left and right modules 2. Injective resolutions 3. The Last term of injective resolution. 4. Purity of injective resolutions 5. Examples 6. Localizations 7. Dualities(More)
Mechanisms of bacterial pathogenesis have become an increasingly important subject as pathogens have become increasingly resistant to current antibiotics. The adhesion of microorganisms to the surface of host tissue is often a first step in pathogenesis and is a plausible target for new antiinfective agents. Examination of bacterial adhesion has been(More)
In 1982 E.K. Sklyanin 13] deened a family of graded algebras A(E;), depending on an elliptic curve E and a point 2 E which is not 4-torsion. Basic properties of these algebras were established in 16], and a study of their representation theory was begun in 7]. The present paper classiies the nite dimensional simple A-modules when is a point of innnite(More)
Let J be a graded ideal in a not necessarily commutative graded k-algebra A = A 0 ⊕ A 1 ⊕ · · · in which dim k A i < ∞ for all i. We show that the map A → A/J induces a closed immersion i : Proj nc A/J → Proj nc A between the non-commutative projective spaces with homogeneous coordinate rings A and A/J. We also examine two other kinds of maps between(More)
We prove a version of B ezout's theorem for non-commutative analogues of the projective spaces P n. 0. Introduction Throughout we work over an algebraically closed eld k. We establish a version of B ezout's Theorem for non-commutative projective spaces, quantum P n s for short. If Y is a quantum P n then the alternating sum of the dimension of the(More)