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.
On the curves of contact on surfaces in a projective space by M. Boratynski Plane sections of curves of low genus by L. Chiantini A moving-lemma for a singular variety and applications to the Grothendieck group $K 0(X)$ by C. Consani The $K$-bcohomology of Enriques surfaces by K. R. Coombes $K$-theory of Henselian local rings and Henselian pairs by O. Gabber On the homological $\pi 0$ of Kac-Moody groups over fields by J. Hurrelbrink, J. Morita, and U. Rehmann The decomposable part of motivic cohomology and bijectivity of the norm residue homomorphism by B. Kahn On the spectral sequence for relative $K$-theory by S. E. Landsburg $G 0$ of integral group rings for groups with cyclic Sylow subgroups by R. C. Laubenbacher and D. L. Webb Deligne-Beilinson cohomology for singular varieties by M. Levine A note on $K 2$ of the rings of integers of totally real number fields by M. Mazur and J. Urbanowicz Intersection points of seminormal configurations of lines by L. Reid and L. G. Roberts Group representations and algebraic $K$-theory: II by C. C. Sherman Remarks on the Stickelberger ideals of order $2$ by J. Urbanowicz Unstable $K 1$-theory of topological spaces is nilpotent by L. N. Vaserstein Cohomology theories and algebraic cycles in singular varieties by L. Viale Localization for the $K$-theory of noncommutative rings by C. Weibel and D. Yao.
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