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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 55; 1994; 676 ppMSC: Primary 14; Secondary 11; 19;
Motives were introduced in the mid1960s 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 AMSIMSSIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of fortyseven papers, from general introductions to specialized surveys to research papers.
This item is also available as part of a set: 
Table of Contents

Articles

Richard M. Hain — Classical polylogarithms [ MR 1265550 ]

A. B. Goncharov — Polylogarithms and motivic Galois groups [ MR 1265551 ]

A. Beĭlinson and P. Deligne — Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs [ MR 1265552 ]

A. Beĭlinson and A. Levin — The elliptic polylogarithm [ MR 1265553 ]

Ralph Greenberg — Iwasawa theory and $p$adic deformations of motives [ MR 1265554 ]

Peter Schneider — $p$adic points of motives [ MR 1265555 ]

A. A. Panchishkin — Admissible nonArchimedean standard zeta functions associated with Siegel modular forms [ MR 1265556 ]

Don Blasius — A $p$adic property of Hodge classes on abelian varieties [ MR 1265557 ]

David Goss — Drinfel′d modules: cohomology and special functions [ MR 1265558 ]

Stephen S. Kudla — The local Langlands correspondence: the nonArchimedean case [ MR 1265559 ]

A. W. Knapp — Local Langlands correspondence: the Archimedean case [ MR 1265560 ]

Dinakar Ramakrishnan — Pure motives and automorphic forms [ MR 1265561 ]

J. S. Milne — Shimura varieties and motives [ MR 1265562 ]

Don Blasius and Jonathan D. Rogawski — Zeta functions of Shimura varieties [ MR 1265563 ]

Michael Harris — Hodgede Rham structures and periods of automorphic forms [ MR 1265564 ]

J. Tilouine — Galois representations congruent to those coming from Shimura varieties [ MR 1265565 ]

Kenneth A. Ribet — Report on mod $l$ representations of $\mathrm {Gal}(\overline {\mathbf {Q}}/\mathbf {Q})$ [ MR 1265566 ]


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Motives were introduced in the mid1960s 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 AMSIMSSIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of fortyseven papers, from general introductions to specialized surveys to research papers.

Articles

Richard M. Hain — Classical polylogarithms [ MR 1265550 ]

A. B. Goncharov — Polylogarithms and motivic Galois groups [ MR 1265551 ]

A. Beĭlinson and P. Deligne — Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs [ MR 1265552 ]

A. Beĭlinson and A. Levin — The elliptic polylogarithm [ MR 1265553 ]

Ralph Greenberg — Iwasawa theory and $p$adic deformations of motives [ MR 1265554 ]

Peter Schneider — $p$adic points of motives [ MR 1265555 ]

A. A. Panchishkin — Admissible nonArchimedean standard zeta functions associated with Siegel modular forms [ MR 1265556 ]

Don Blasius — A $p$adic property of Hodge classes on abelian varieties [ MR 1265557 ]

David Goss — Drinfel′d modules: cohomology and special functions [ MR 1265558 ]

Stephen S. Kudla — The local Langlands correspondence: the nonArchimedean case [ MR 1265559 ]

A. W. Knapp — Local Langlands correspondence: the Archimedean case [ MR 1265560 ]

Dinakar Ramakrishnan — Pure motives and automorphic forms [ MR 1265561 ]

J. S. Milne — Shimura varieties and motives [ MR 1265562 ]

Don Blasius and Jonathan D. Rogawski — Zeta functions of Shimura varieties [ MR 1265563 ]

Michael Harris — Hodgede Rham structures and periods of automorphic forms [ MR 1265564 ]

J. Tilouine — Galois representations congruent to those coming from Shimura varieties [ MR 1265565 ]

Kenneth A. Ribet — Report on mod $l$ representations of $\mathrm {Gal}(\overline {\mathbf {Q}}/\mathbf {Q})$ [ MR 1265566 ]