## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, February 13, 2018 — 3:00 PM EST

**David Urbanik, Department of Pure Mathematics, University of Waterloo**

"Chevalley's Theorem on Constructible Sets in the Language of Schemes"

We continue working through Vakil's notes, this time covering section 7.4 on Chevalley's Theorem on Constructible Sets. Chevalley's theorem gives a sensible answer to the question: given a sufficiently "nice" scheme X and a correspondingly "nice" morphism X to Y, what can we say about the image of X in Y? The answer is that the image is a so-called "constructible set", which we will see is a natural notion that generalizes open and closed sets. Chevalley's theorem will also give us a proof of the Nullstellensatz, and help us develop intuition for the types of scheme morphisms we have defined so far.

MC 5417

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

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