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

Ehsaan Hossain, Pure Mathematics, University of Waterloo

"Hilbert's Syzygy Theorem"

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

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