Motives, Part 1
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.
What people are saying - Write a review
We haven't found any reviews in the usual places.
On the Bijectivity of Some Cycle Maps
Propriétés conjecturales des groupes de Galois motiviques et
Motives over Finite Fields
Motives for Absolute Hodge Cycles
Motives and the Taniyama Group
Structures de Hodge mixtes réelles
Arithmetic Analogs of the Standard Conjectures
A quoi servent les motifs?
On the Chow Motive of an Abelian Scheme
Weight Filtrations in Algebraic K Theory
An Elementary Presentation for K Groups and Motivic Cohomology
Motivic Sheaves and Filtrations on Chow Groups
LFunctions of Mixed Motives
LFunctions at the Central Critical Point
Height Pairings and Special Values of LFunctions
Report on mod Representations of GalQQ
Motivic LFunctions and Regularized Determinants
On a Result of Deninger Concerning Riemanns Zeta Function
Other editions - View all
abelian varieties action acts algebraic algebraic cycles associated assume Beilinson called canonical character Chow closed cohomology commutative compatible complex condition conjecture consider construction corresponding curves deﬁned deﬁnition Deligne denote determined dimension direct discussion element equal equivalence étale example exists extension fact factor ﬁbre functor ﬁeld ﬁltration ﬁnite ﬁrst follows formula function Galois geometric gerbe given gives Grothendieck Hence Hodge structure holds homomorphism implies induced integer isomorphism L-functions LEMMA Math mixed motives modules morphism motifs motives multiplication natural object obtain operations pair projective PROOF properties PROPOSITION proved pure rational REMARK representations resp respect restriction result ring satisfying scheme smooth space standard Tannakian category Tate tensor theorem theory trivial unique values weight York zero