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Motives: Part 1
 
Edited by: Uwe Jannsen
Steven Kleiman
Jean-Pierre Serre

Also Available in Softcover
Softcover ISBN:  978-0-8218-2797-0
Product Code:  PSPUM/55.1.S
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eBook ISBN:  978-0-8218-9355-5
Product Code:  PSPUM/55.1.E
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AMS Member Price: $108.00
Softcover ISBN:  978-0-8218-2797-0
eBook: ISBN:  978-0-8218-9355-5
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Motives: Part 1
Edited by: Uwe Jannsen
Steven Kleiman
Jean-Pierre Serre

Also Available in Softcover
Softcover ISBN:  978-0-8218-2797-0
Product Code:  PSPUM/55.1.S
List Price: $139.00
MAA Member Price: $125.10
AMS Member Price: $111.20
eBook ISBN:  978-0-8218-9355-5
Product Code:  PSPUM/55.1.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-0-8218-2797-0
eBook ISBN:  978-0-8218-9355-5
Product Code:  PSPUM/55.1.S.B
List Price: $274.00 $206.50
MAA Member Price: $246.60 $185.85
AMS Member Price: $219.20 $165.20
Add to cart
  • Book Details
     
     
    Proceedings of Symposia in Pure Mathematics
    Volume: 55; 1994; 747 pp
    MSC: Primary 14; Secondary 11; 19

    Motives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field. Over the last ten years or so, researchers in various areas—Hodge theory, algebraic \(K\)-theory, polylogarithms, automorphic forms, \(L\)-functions, \(\ell\)-adic representations, trigonometric sums, and algebraic cycles—have discovered that an enlarged (and in part conjectural) theory of “mixed” motives indicates and explains phenomena appearing in each area. Thus the theory holds the potential of enriching and unifying these areas. This is one of two volumes containing the revised texts of nearly all the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.
    This item is also available as part of a set:
  • Table of Contents
     
     
    • Articles
    • Steven L. Kleiman — The standard conjectures [ MR 1265519 ]
    • Nicholas M. Katz — Review of $l$-adic cohomology [ MR 1265520 ]
    • J. H. M. Steenbrink — A summary of mixed Hodge theory [ MR 1265521 ]
    • Luc Illusie — Crystalline cohomology [ MR 1265522 ]
    • John Tate — Conjectures on algebraic cycles in $l$-adic cohomology [ MR 1265523 ]
    • Morihiko Saito — Some remarks on the Hodge type conjecture [ MR 1265524 ]
    • Nicholas M. Katz — Independence of $l$ and weak Lefschetz [ MR 1265525 ]
    • Pierre Deligne — Décompositions dans la catégorie dérivée [ MR 1265526 ]
    • H. Gillet and C. Soulé — Arithmetic analogs of the standard conjectures [ MR 1265527 ]
    • Pierre Deligne — À quoi servent les motifs? [ MR 1265528 ]
    • A. J. Scholl — Classical motives [ MR 1265529 ]
    • Klaus Künnemann — On the Chow motive of an abelian scheme [ MR 1265530 ]
    • Daniel R. Grayson — Weight filtrations in algebraic $K$-theory [ MR 1265531 ]
    • Spencer Bloch — An elementary presentation for $K$-groups and motivic cohomology [ MR 1265532 ]
    • Uwe Jannsen — Motivic sheaves and filtrations on Chow groups [ MR 1265533 ]
    • Stephen Lichtenbaum — Motivic complexes [ MR 1265534 ]
    • Morihiko Saito — On the bijectivity of some cycle maps [ MR 1265535 ]
    • Lawrence Breen — Tannakian categories [ MR 1265536 ]
    • Jean-Pierre Serre — Propriétés conjecturales des groupes de Galois motiviques et des représentations $l$-adiques [ MR 1265537 ]
    • J. S. Milne — Motives over finite fields [ MR 1265538 ]
    • A. A. Panchishkin — Motives for absolute Hodge cycles [ MR 1265539 ]
    • Norbert Schappacher — CM motives and the Taniyama group [ MR 1265540 ]
    • Pierre Deligne — Structures de Hodge mixtes réelles [ MR 1265541 ]
    • Christopher Deninger — $L$-functions of mixed motives [ MR 1265542 ]
    • Benedict H. Gross — $L$-functions at the central critical point [ MR 1265543 ]
    • Jan Nekovář — Beĭlinson’s conjectures [ MR 1265544 ]
    • A. J. Scholl — Height pairings and special values of $L$-functions [ MR 1265545 ]
    • Jean-Marc Fontaine and Bernadette Perrin-Riou — Autour des conjectures de Bloch et Kato: cohomologie galoisienne et valeurs de fonctions $L$ [ MR 1265546 ]
    • Christopher Deninger — Motivic $L$-functions and regularized determinants [ MR 1265547 ]
    • M. Schröter and C. Soulé — On a result of Deninger concerning Riemann’s zeta function [ MR 1265548 ]
  • 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
Proceedings of Symposia in Pure Mathematics
Volume: 55; 1994; 747 pp
MSC: Primary 14; Secondary 11; 19

Motives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field. Over the last ten years or so, researchers in various areas—Hodge theory, algebraic \(K\)-theory, polylogarithms, automorphic forms, \(L\)-functions, \(\ell\)-adic representations, trigonometric sums, and algebraic cycles—have discovered that an enlarged (and in part conjectural) theory of “mixed” motives indicates and explains phenomena appearing in each area. Thus the theory holds the potential of enriching and unifying these areas. This is one of two volumes containing the revised texts of nearly all the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.
This item is also available as part of a set:
  • Articles
  • Steven L. Kleiman — The standard conjectures [ MR 1265519 ]
  • Nicholas M. Katz — Review of $l$-adic cohomology [ MR 1265520 ]
  • J. H. M. Steenbrink — A summary of mixed Hodge theory [ MR 1265521 ]
  • Luc Illusie — Crystalline cohomology [ MR 1265522 ]
  • John Tate — Conjectures on algebraic cycles in $l$-adic cohomology [ MR 1265523 ]
  • Morihiko Saito — Some remarks on the Hodge type conjecture [ MR 1265524 ]
  • Nicholas M. Katz — Independence of $l$ and weak Lefschetz [ MR 1265525 ]
  • Pierre Deligne — Décompositions dans la catégorie dérivée [ MR 1265526 ]
  • H. Gillet and C. Soulé — Arithmetic analogs of the standard conjectures [ MR 1265527 ]
  • Pierre Deligne — À quoi servent les motifs? [ MR 1265528 ]
  • A. J. Scholl — Classical motives [ MR 1265529 ]
  • Klaus Künnemann — On the Chow motive of an abelian scheme [ MR 1265530 ]
  • Daniel R. Grayson — Weight filtrations in algebraic $K$-theory [ MR 1265531 ]
  • Spencer Bloch — An elementary presentation for $K$-groups and motivic cohomology [ MR 1265532 ]
  • Uwe Jannsen — Motivic sheaves and filtrations on Chow groups [ MR 1265533 ]
  • Stephen Lichtenbaum — Motivic complexes [ MR 1265534 ]
  • Morihiko Saito — On the bijectivity of some cycle maps [ MR 1265535 ]
  • Lawrence Breen — Tannakian categories [ MR 1265536 ]
  • Jean-Pierre Serre — Propriétés conjecturales des groupes de Galois motiviques et des représentations $l$-adiques [ MR 1265537 ]
  • J. S. Milne — Motives over finite fields [ MR 1265538 ]
  • A. A. Panchishkin — Motives for absolute Hodge cycles [ MR 1265539 ]
  • Norbert Schappacher — CM motives and the Taniyama group [ MR 1265540 ]
  • Pierre Deligne — Structures de Hodge mixtes réelles [ MR 1265541 ]
  • Christopher Deninger — $L$-functions of mixed motives [ MR 1265542 ]
  • Benedict H. Gross — $L$-functions at the central critical point [ MR 1265543 ]
  • Jan Nekovář — Beĭlinson’s conjectures [ MR 1265544 ]
  • A. J. Scholl — Height pairings and special values of $L$-functions [ MR 1265545 ]
  • Jean-Marc Fontaine and Bernadette Perrin-Riou — Autour des conjectures de Bloch et Kato: cohomologie galoisienne et valeurs de fonctions $L$ [ MR 1265546 ]
  • Christopher Deninger — Motivic $L$-functions and regularized determinants [ MR 1265547 ]
  • M. Schröter and C. Soulé — On a result of Deninger concerning Riemann’s zeta function [ MR 1265548 ]
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Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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