Christian Haesemeyer : Du Bois invariants of singularities and a question of Bass

Posted by , part of the Algebraic Geometry Seminar.

At

Sept. 6, 2007, 4 p.m.

In

SEO 636

Abstract

If the Picard group of a Noetherian ring R is equal to that of R[t], then it stays the same for polynomial rings over R in any number of variables. Bass asked if the same is true for the Grothendieck group of vector bundles, or more generally for any algebraic K-group. I will report on joint work with Cortinas, Walker and Weibel that answers this question; it turns out that the cohomology of the du Bois complexes appears as a summand in the K-groups, and classical computations of du Bois invariants of semiquasihomogeneous surface singularities over the rationals provide examples for which the answer is \"no\".