# Algebra seminar

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

### February 2020

S M T W T F S
26
27
28
29
30
31
1
2
3
8
9
13
15
16
17
19
20
21
22
23
25
26
27
28
29
1. 2020 (39)
1. February (17)
2. January (22)
2. 2019 (199)
1. December (7)
2. November (26)
3. October (19)
4. September (13)
5. August (7)
6. July (12)
7. June (18)
8. May (22)
9. April (11)
10. March (25)
11. February (17)
12. January (22)
3. 2018 (219)
4. 2017 (281)
5. 2016 (335)
6. 2015 (209)
7. 2014 (235)
8. 2013 (251)
9. 2012 (135)