## 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

Wednesday, January 14, 2015 — 2:30 PM EST

Last semester we studied the group $K_0$, whose elements are stable equivalence classes of projective modules. Tangent to this, I want to discuss the Quillen--Suslin Theorem, which states that every finitely-generated projective module over a polynomial ring $k[x_1,\ldots,x_n]$ is free. On the topological side, this says every algebraic vector bundle over affine $n$-space is free. Vaserstein gave a shorter, elementary proof of the Q--S Theorem, so we'll be going over some of the prerequisites. Our first goal is to show every projective module over a polynomial ring is stably-free.

Location

MC - Mathematics & Computer Building

5403

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

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.