The seminar meets Fridays, 3:00--4:00pm, in LCB 222.

February 3, 2006:

(1) For another R-module N, if Tor_i(M,N)=0 then Tor_j(M,N)= 0 for j>i. (2) If N is such that M_tensor N has finite length, then dim M + dim N <= dim R. These properties have been studied over the years, with the classical view that they "should" hold when M has finite projective dimension. We will present some recent results that show a connection between the two, as well as some K-theoretic sufficient conditions for them. We will also discuss some open questions, which are linked to conjectures about Chow group of smooth projective hypersurfaces in P^n.

February 17, 2006: (Joint
seminar with Number Theory)

February 24, 2006:

March 3, 2006:

March 6, 2006: (Special
Monday seminar in JWB 208 at 2pm)

March 10, 2006:

March 24, 2006:

March 31, 2006:

April 7, 2006:

April 14, 2006:

April 21, 2006:

September
2, 2005:

September
9, 2005:

September
16, 2005:

September
23, 2005

September
30, 2005

October
14, 2005

October
21, 2005

October
28, 2005

November
4, 2005

November
11, 2005

November
18, 2005:

December
2, 2005:

December
9, 2005:

**Monday**,
December
12, 2005 at **1pm**
in LCB 323:

January
21, 2005:

January
28, 2005:

February
4, 2005:

February
11, 2005:

February
18, 2005:

February
25, 2005:

March
4, 2005:

March
11, 2005:

March
18, 2005:

March
25, 2005:

commutative algebra, these homological dimensions are used to characterize

Gorenstein rings in much the same way the usual homological dimensions

characterize regular rings.

The study of Gorenstein dimensions takes cues from the theory of classical

homological dimensions. However, while the results may be parallel, the proofs

are sometimes very different. The talk will illustrate this by considering some

questions on stability of Gorenstein dimensions.

April
1, 2005:

April
8, 2005:

April
15, 2005:

N are modules of finite length and finite projective dimension, and if

dim (M) + dim (N) < d = dim (A), then the intersection multiplicity of M and N = 0.

Much work has been done to try to determine when the vanishing conjecture

holds. Roberts and Srinivas determined correspondences between

intersection properties of modules of finite length and finite projective

dimension and the Chow group of the ring in their paper entitled Modules

of finite length and finite projective dimension.

April
22, 2005:

September
3, 2004:

September
10, 2004:

September
24, 2004:

October
1, 2004:

October
22, 2004:

October
29, 2004:

November
12, 2004:

November
19, 2004

August
29, 2003:

September
5, 2003:

September
12, 2003:

September
19, 2003:

September
26, 2003:

October
10, 2003:

October
24, 2003:

October 31, 2003:

November 7, 2003:

November 21, 2003: