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Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry
 
Edited by: R. Keith Dennis Mathematical Reviews, Ann Arbor, MI
Claudio Pedrini University of Genova, Genoa, Italy
Michael R. Stein Northwestern University, Evanston, IL
Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry
eBook ISBN:  978-0-8218-7714-2
Product Code:  CONM/126.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry
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Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry
Edited by: R. Keith Dennis Mathematical Reviews, Ann Arbor, MI
Claudio Pedrini University of Genova, Genoa, Italy
Michael R. Stein Northwestern University, Evanston, IL
eBook ISBN:  978-0-8218-7714-2
Product Code:  CONM/126.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1261992; 230 pp
    MSC: Primary 13; 14; 19

    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
     
     
    • Articles
    • M. Boratyński — On the curves of contact on surfaces in a projective space [ MR 1156498 ]
    • Luca Chiantini — Plane sections of curves of low genus [ MR 1156499 ]
    • Caterina Consani — A moving-lemma for a singular variety and applications to the Grothendieck group $K_0(X)$ [ MR 1156500 ]
    • Kevin R. Coombes — The $K$-cohomology of Enriques surfaces [ MR 1156501 ]
    • Ofer Gabber — $K$-theory of Henselian local rings and Henselian pairs [ MR 1156502 ]
    • Jürgen Hurrelbrink, Jun Morita and Ulf Rehmann — On the homological $\pi _0$ of Kac-Moody groups over fields [ MR 1156503 ]
    • Bruno Kahn — The decomposable part of motivic cohomology and bijectivity of the norm residue homomorphism [ MR 1156504 ]
    • Steven E. Landsburg — On the spectral sequence for relative $K$-theory [ MR 1156505 ]
    • Reinhard C. Laubenbacher and David L. Webb — $G_0$ of integral group rings for groups with cyclic Sylow subgroups [ MR 1156506 ]
    • Marc Levine — Deligne-Beĭlinson cohomology for singular varieties [ MR 1156507 ]
    • Marcin Mazur and Jerzy Urbanowicz — A note on $K_2$ of the rings of integers of totally real number fields [ MR 1156508 ]
    • Les Reid and Leslie G. Roberts — Intersection points of seminormal configurations of lines [ MR 1156509 ]
    • Clayton Sherman — Group representations and algebraic $K$-theory. II [ MR 1156510 ]
    • Jerzy Urbanowicz — Remarks on the Stickelberger ideals of order $2$ [ MR 1156511 ]
    • L. N. Vaserstein — Unstable $K_1$-theory of topological spaces is nilpotent [ MR 1156512 ]
    • Luca Barbieri Viale — Cohomology theories and algebraic cycles on singular varieties [ MR 1156513 ]
    • Charles Weibel and Dongyuan Yao — Localization for the $K$-theory of noncommutative rings [ MR 1156514 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1261992; 230 pp
MSC: Primary 13; 14; 19

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.

  • Articles
  • M. Boratyński — On the curves of contact on surfaces in a projective space [ MR 1156498 ]
  • Luca Chiantini — Plane sections of curves of low genus [ MR 1156499 ]
  • Caterina Consani — A moving-lemma for a singular variety and applications to the Grothendieck group $K_0(X)$ [ MR 1156500 ]
  • Kevin R. Coombes — The $K$-cohomology of Enriques surfaces [ MR 1156501 ]
  • Ofer Gabber — $K$-theory of Henselian local rings and Henselian pairs [ MR 1156502 ]
  • Jürgen Hurrelbrink, Jun Morita and Ulf Rehmann — On the homological $\pi _0$ of Kac-Moody groups over fields [ MR 1156503 ]
  • Bruno Kahn — The decomposable part of motivic cohomology and bijectivity of the norm residue homomorphism [ MR 1156504 ]
  • Steven E. Landsburg — On the spectral sequence for relative $K$-theory [ MR 1156505 ]
  • Reinhard C. Laubenbacher and David L. Webb — $G_0$ of integral group rings for groups with cyclic Sylow subgroups [ MR 1156506 ]
  • Marc Levine — Deligne-Beĭlinson cohomology for singular varieties [ MR 1156507 ]
  • Marcin Mazur and Jerzy Urbanowicz — A note on $K_2$ of the rings of integers of totally real number fields [ MR 1156508 ]
  • Les Reid and Leslie G. Roberts — Intersection points of seminormal configurations of lines [ MR 1156509 ]
  • Clayton Sherman — Group representations and algebraic $K$-theory. II [ MR 1156510 ]
  • Jerzy Urbanowicz — Remarks on the Stickelberger ideals of order $2$ [ MR 1156511 ]
  • L. N. Vaserstein — Unstable $K_1$-theory of topological spaces is nilpotent [ MR 1156512 ]
  • Luca Barbieri Viale — Cohomology theories and algebraic cycles on singular varieties [ MR 1156513 ]
  • Charles Weibel and Dongyuan Yao — Localization for the $K$-theory of noncommutative rings [ MR 1156514 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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