Motives, Part 1

Front Cover
American Mathematical Soc., 1994 - Mathematics - 747 pages
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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Contents

PART
3
Review of éadic Cohomology
21
A Summary of Mixed Hodge Theory
31
Crystalline Cohomology
43
Conjectures on Algebraic Cycles in ladic Cohomology
71
Some Remarks on the Hodge Type Conjecture
85
Independence of Z and Weak Lefschetz
101
Décompositions dans la catégorie dérivée
115
Motivic Complexes
301
On the Bijectivity of Some Cycle Maps
315
Tannakian Categories
337
Propriétés conjecturales des groupes de Galois motiviques et
377
Motives over Finite Fields
401
Motives for Absolute Hodge Cycles
461
Motives and the Taniyama Group
482
Structures de Hodge mixtes réelles
509

Arithmetic Analogs of the Standard Conjectures
129
A quoi servent les motifs?
143
Classical Motives
163
cohomologie galoisienne
186
On the Chow Motive of an Abelian Scheme
189
Weight Filtrations in Algebraic K Theory
207
An Elementary Presentation for K Groups and Motivic Cohomology
239
Motivic Sheaves and Filtrations on Chow Groups
245
LFunctions of Mixed Motives
517
LFunctions at the Central Critical Point
527
Beilinsons Conjectures
537
Height Pairings and Special Values of LFunctions
570
Report on mod Representations of GalQQ
639
Motivic LFunctions and Regularized Determinants
707
On a Result of Deninger Concerning Riemanns Zeta Function
745
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