Algebraic geometry working seminar

Catherine St-Pierre, University of Waterloo

Why does the Spec functor not extend to non-commutative rings?

The functor Spec, which assigns to a commutative ring its prime spectrum, plays a central role in algebraicgeometry. A natural question is whether this construction can be extended in a meaningful way tononcommutative rings. In this talk, we discuss the obstruction to the extension of the functor Spec to non-commutative rings presented by Manuel L. Reyes, showing that any functor extending Spec and satisfyingreasonable compatibility conditions must collapse on certain noncommutative rings, such as matrix algebras$M_3(\mathbb C)$.

MC 5417