# Algebraic \(K\)-Theory, Commutative Algebra, and Algebraic Geometry

Share this page *Edited by *
*R. Keith Dennis; Claudio Pedrini; Michael R. Stein*

In the mid-1960s, several Italian mathematicians began to study the
connections between classical arguments in commutative algebra and algebraic
geometry, and the contemporaneous development of algebraic \(K\)-theory
in the U.S. These connections were exemplified by the work of
Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy
on the Picard groups of polynomial rings. Interactions proceeded far beyond
this initial point to encompass Chow groups of singular varieties, complete
intersections, and applications of \(K\)-theory to arithmetic and real
geometry.

This volume contains the proceedings from a U.S.–Italy Joint Summer
Seminar, which focused on this circle of ideas. The conference, held in June
1989 in Santa Margherita Ligure, Italy, was supported jointly by the Consiglio
Nazionale delle Ricerche and the National Science Foundation. The book
contains contributions from some of the leading experts in this area.

# Table of Contents

## Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry

- Contents v6 free
- Preface vii8 free
- List of participants ix10 free
- On the curves of contact on surfaces in a projective space 118 free
- Plane sections of curves of low genus 926
- A moving-lemma for a singular variety and applications to the Grothendieck group K0(X) 2138
- The K-cohomology of Enriques surfaces 4764
- K-theory of Henselian local rings and Henselian pairs 5976
- On the homological π0 of Kac-Moody groups over fields 7188
- The decomposable part of motivic cohomology and bijectivity of the norm residue homomorphism 7996
- On the spectral sequence for relative K-theory 89106
- G0 of integral group rings for groups with cyclic Sylow subgroups 97114
- Deligne-Beilinson cohomology for singular varieties 113130
- A note on K2 of the rings of integers of totally real number fields 147164
- Intersection points of seminormal configurations of lines 151168
- Group representations and algebraic K-theory: II 165182
- Remarks on the Stickelberger ideals of order 2 179196
- Unstable K1-theory of topological spaces is nilpotent 193210
- Cohomology theories and algebraic cycles in singular varieties 197214
- Localization for the K-theory of noncommutative rings 219236