## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, May 31, 2012 — 1:00 PM to 2:00 PM EDT

For a ring R, let Spec(R) denote the set of its prime ideals. We are going to topologize Spec(R) by demanding that R is the ring of continuous functions (into where?) defined on Spec(R). This is called the Zariski Topology. It is so named because, in the case that R is the coordinate ring of an affine variety X, we will see that Spec(R) is almost equal to (whatever that means) X, and that the topology on Spec(R) is almost the same as the usual Zariski topology on X. This is the first step in saying what a scheme is.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.