May 23, 2000

Rob de Jeu

Title: Homology of GL_n and the rank conjecture

Abstract:

The rank conjecture relates the filtration on the K-theory of a field obtained from the inclusion of GL_n into GL_n+1 to the weights on the K-theory. We show the rank conjecture is equivalent to a sharper statement, and give applications of this sharper statement to obtain another conjecture about the relation to Bloch's higher Chow groups. We prove part of this new conjecture.