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Cycles, motives and shimura varieties : proceedings / [edited by] V. Srinivas.

By: Contributor(s): Series: Studies in mathematics (Tata Institute of Fundamental Research) ; 21Publication details: New Delhi : Narosa Publishing House, c2010.Description: x, 530 p. : illustrations ; 25 cmISBN:
  • 9788184870855
Subject(s): DDC classification:
  • 23 In61 512.72
Contents:
Machine generated contents note: Mixed Hodge Structures Associated to Geometric Variations / Donu Arapura -- Beilinson's Tate Conjecture for K2 of Elliptic Surface: Survey and Examples / Kanetomo Sato -- On the Freeness of the Integral Cohomology Groups of Hilbert-Blumenthal Varieties as Hecke Modules / Eknath Ghate -- Singularities of Admissable Normal Functions / Phillip Griffiths -- Arithmetic Aspects of Rank One Eisenstein Cohomology / G. Harder -- Appendix: On Harder's S1(2, R) -S1(3, R) -- identity / Don Zagier -- Beilinson's Hodge Conjecture for K1 Revisited / James D. Lewis -- A Remark on the Second Abel-Jacobi Map / Kenichiro Kimura -- On Natural Isomorphisms of Finite Dimensional Motives and Applications to the Picard Motives / Jacob P. Murre -- Zero Cycles on Singular Affine Varieties / V. Srinivas -- Tate Motives and The Fundamental Group / Marc Levine -- Chow Motives of Mixed Shimura Varieties / Andrea Miller -- Dualizing Complexes -- The Modern Way / Amnon Neeman -- The Griffiths Group of the Generic Abelian 3-fold / V. Srinivas -- Non-Archimedcan Regulator Maps and Special Values of L-functions / Ramesh Sreckantan-- The Artin-Schreier DGA and the Fp fundamental group of an Fp scheme / Tomohide Terasoma.
Summary: This volume covers the proceedings of the International Colloquium organised by the Tata Institute of Fundamental Research in January 2008, one of a series of Colloquia going back to 1956. It covers a wide spectrum of mathematics, ranging over algebraic geometry, topology, automorphic forms and number theory. Algebraic cycles form the basis for the construction of Motives, and conjectures about Motives depend ultimately on important problems related to algebraic cycles, like the Hodge and the Tata Conjectures. Shimura Varieties provide interesting, nontrivial instances of these fundamental problems. On the other hand, the Motives of Shimura Varieties are of great interest in automorphic forms and number theory. This book contains refereed articles by leading experts in these fields, containing original results, as well as expository material, on these areas.
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Machine generated contents note: Mixed Hodge Structures Associated to Geometric Variations / Donu Arapura --
Beilinson's Tate Conjecture for K2 of Elliptic Surface: Survey and Examples / Kanetomo Sato --
On the Freeness of the Integral Cohomology Groups of Hilbert-Blumenthal Varieties as Hecke Modules / Eknath Ghate --
Singularities of Admissable Normal Functions / Phillip Griffiths --
Arithmetic Aspects of Rank One Eisenstein Cohomology / G. Harder --
Appendix: On Harder's S1(2, R) -S1(3, R) --
identity / Don Zagier --
Beilinson's Hodge Conjecture for K1 Revisited / James D. Lewis --
A Remark on the Second Abel-Jacobi Map / Kenichiro Kimura --
On Natural Isomorphisms of Finite Dimensional Motives and Applications to the Picard Motives / Jacob P. Murre --
Zero Cycles on Singular Affine Varieties / V. Srinivas --
Tate Motives and The Fundamental Group / Marc Levine --
Chow Motives of Mixed Shimura Varieties / Andrea Miller --
Dualizing Complexes --
The Modern Way / Amnon Neeman --
The Griffiths Group of the Generic Abelian 3-fold / V. Srinivas --
Non-Archimedcan Regulator Maps and Special Values of L-functions / Ramesh Sreckantan--
The Artin-Schreier DGA and the Fp fundamental group of an Fp scheme / Tomohide Terasoma.

This volume covers the proceedings of the International Colloquium organised by the Tata Institute of Fundamental Research in January 2008, one of a series of Colloquia going back to 1956. It covers a wide spectrum of mathematics, ranging over algebraic geometry, topology, automorphic forms and number theory. Algebraic cycles form the basis for the construction of Motives, and conjectures about Motives depend ultimately on important problems related to algebraic cycles, like the Hodge and the Tata Conjectures. Shimura Varieties provide interesting, nontrivial instances of these fundamental problems. On the other hand, the Motives of Shimura Varieties are of great interest in automorphic forms and number theory. This book contains refereed articles by leading experts in these fields, containing original results, as well as expository material, on these areas.

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