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: set ISBN 9780821816356
内容説明
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 abou 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, 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. These volumes contain the revised texts of nearly all the lectures presented a the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle in 1991. A number of related works ae also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers. This book is intended for research mathematicians.
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pt. 1 ISBN 9780821816363
内容説明
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.
目次
Part 1. Cohomology: The standard conjectures by S. Kleiman Review of $\ell$-adic cohomology by N. M. Katz A summary of mixed Hodge theory by J. H. M. Steenbrink Crystalline cohomology by L. Illusie Conjectures on algebraic cycles in $\ell$-adic cohomology by J. Tate Some remarks on the Hodge type conjecture by M. Saito Independence of $\ell$ and weak Lefschetz by N. M. Katz Decompositions dans la categorie derivee by P. Deligne Arithmetic analogs of the standard conjectures by H. Gillet and C. Soule Chow groups, $K$-theory and motivic cohomology A quoi servent les motifs? by P. Deligne Classical motives by A. J. Scholl On the Chow motive of an abelian scheme by K. Kunnemann Weight filtrations in algebraic $K$-theory by D. R. Grayson An elementary presentation for $K$-groups and motivic cohomology by S. Bloch Motivic sheaves and filtrations on Chow groups by U. Jannsen Motivic complexes by S. Lichtenbaum On the bijectivity of some cycle maps by M. Saito Motivic Galois groups Tannakian categories by L. Breen Proprietes conjecturales des groupes de Galois motiviques et des representations $\ell$-adiques by J.-P. Serre Motives over finite fields by J. S. Milne Motives for absolute Hodge cycles by A. A. Panchishkin CM motives and the Taniyama group by N. Schappacher Structures de Hodge mixtes reelles by P. Deligne $L$-functions $L$-functions of mixed motives by C. Deninger $L$-functions at the central critical point by B. H. Gross Beilinson's conjectures by J. Nekovar Height pairings and special values of $L$-functions by A. J. Scholl Autours des conjectures de Bloch et Kato: Cohomologie galoisienne et valeurs de fonctions $L$ by J.-M. Fontaine and B. Perrin-Riou Motivic $L$-functions and regularized determinants by C. Deninger On a result of Deninger concerning Riemann's zeta function by M. Schroter and C. Soule.
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pt. 2 ISBN 9780821816370
内容説明
These volumes contain 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.
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pt. 2 : pbk. ISBN 9780821827987
内容説明
'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.
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: pbk. set ISBN 9780821827994
内容説明
'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. These two volumes contain 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.
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