Daniel Chan (University of New South Wales)

Friday 8th September, 12.05-12.55pm, Carslaw 373

Explicit non-commutative geometry

Orders in central simple algebras provide examples of non-commutative algebro-geometric objects. When the centre of the order is a projective surface, they have been studied indirectly via ramification data. Such "non-commutative surfaces" have not been directly studied, in part, because of the lack of explicit examples. In this talk we give a construction of orders on projective surfaces using Van den Bergh's notion of a bimodule over a scheme. We give some applications of this construction such as the computation of some moduli spaces of line bundles over an order.

The talk will assume a modest acquaintance with algebraic geometry but will otherwise be elementary.