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Algebraic $$K$$-Theory, Commutative Algebra, and Algebraic Geometry
Edited by: R. Keith Dennis, Claudio Pedrini, and Michael R. Stein
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Contemporary Mathematics
1992; 230 pp; softcover
Volume: 126
ISBN-10: 0-8218-5130-6
ISBN-13: 978-0-8218-5130-2
List Price: US$71 Member Price: US$56.80
Order Code: CONM/126

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.

• M. Boratynski -- On the curves of contact on surfaces in a projective space
• L. Chiantini -- Plane sections of curves of low genus
• C. Consani -- A moving-lemma for a singular variety and applications to the Grothendieck group $$K_0(X)$$
• K. R. Coombes -- The $$K$$-bcohomology of Enriques surfaces
• O. Gabber -- $$K$$-theory of Henselian local rings and Henselian pairs
• J. Hurrelbrink, J. Morita, and U. Rehmann -- On the homological $$\pi_0$$ of Kac-Moody groups over fields
• B. Kahn -- The decomposable part of motivic cohomology and bijectivity of the norm residue homomorphism
• S. E. Landsburg -- On the spectral sequence for relative $$K$$-theory
• R. C. Laubenbacher and D. L. Webb -- $$G_0$$ of integral group rings for groups with cyclic Sylow subgroups
• M. Levine -- Deligne-Beilinson cohomology for singular varieties
• M. Mazur and J. Urbanowicz -- A note on $$K_2$$ of the rings of integers of totally real number fields
• L. Reid and L. G. Roberts -- Intersection points of seminormal configurations of lines
• C. C. Sherman -- Group representations and algebraic $$K$$-theory: II
• J. Urbanowicz -- Remarks on the Stickelberger ideals of order $$2$$
• L. N. Vaserstein -- Unstable $$K_1$$-theory of topological spaces is nilpotent
• L. Viale -- Cohomology theories and algebraic cycles in singular varieties
• C. Weibel and D. Yao -- Localization for the $$K$$-theory of noncommutative rings