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THE WORK OF JAN-ERIK ROOS ON THE COHOMOLOGY OF COMMUTATIVE RINGS
 

Summary: THE WORK OF JAN-ERIK ROOS ON
THE COHOMOLOGY OF COMMUTATIVE RINGS
LUCHEZAR L. AVRAMOV
This is an attempt to present one aspect of the work of Jan-Erik Roos.
A glance at the list of publications reveals three clearly defined periods in his
life as an algebraist. During the first one he studied abelian categories, obtaining
fundamental results on derived functors of inverse limits. They are contained in
[3], [5]­[9], [11]­[17], [19]­[21]. In the second period he focused on the homological
theory of non-commutative rings, producing methods and results of lasting interest,
among them a truly classic theorem--the determination of the global dimension of
Weyl algebras. The papers [4], [18], [22]­[26], and [31] (treating related questions
from commutative ring theory) contain the results of that period. Bjšork [Bj] has
given an overview in the context of contemporary and subsequent research.
The work discussed here starts in the mid-1970s, when Jan-Erik turned to homo-
logical problems on finitely generated modules over commutative noetherian local
(or graded) rings. He has produced fascinating results on the structure of free res-
olutions of modules of infinite projective dimension, and has investigated deep and
mysterious links between homological properties of commutative rings and topo-
logical spaces. His study of numerical invariants encoded in PoincarŽe series, and
of algebraic invariants determined by Yoneda products and by homology products,

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics