CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Professor Alex Tchernev  
Time & Place:  Wednesday, November 8, at 4:30pm, in ES 152A  
Title:         Free resolutions for polynomial functors
               (Continued) 


Abstract: 

Let $L$ be a homogeneous polynomial functor from finite free 
modules to finite free modules (e.g. $L=S^k$ or $L=\wedge^k$). 
We investigate two different canonical ways $C_L$ and $D_L$ of 
prolonging $L$ to a functor from finite free complexes to 
finite free complexes. Given a finite free complex $F$, 
we provide a criterion for the acyclicity of $C_L(F)$, 
and a criterion for the acyclicity of $D_L(F)$. As an 
application we give a proof in general of the Buchsbaum-Eisenbud 
conjecture on the structure of the lower order minors of the 
differentials in a finite free resolution. This conjecture was 
previously known only in characteristic zero.  

(This is joint work with Jerzy Weyman.)


Refreshments at 4:15pm in ES 152.