| Description |
1 online resource (xiv, 292 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
London Mathematical Society lecture note series ; 343
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London Mathematical Society lecture note series ; 343.
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| Bibliography |
Includes bibliographical references. |
| Summary |
Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity. This 2007 book is one of two volumes that provide a self-contained account of the subject. Together, the two books contain twenty-two contributions from leading figures in the field which survey the key research strands and present interesting new results. Topics discussed include: the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers and students in complex algebraic geometry and arithmetic geometry will find much of interest here. |
| Contents |
Cover; Title; Copyright; Contents of Volume 1; Preface; Volume 1: Survey Articles ; 1 The Motivic Vanishing Cycles and the Conservation Conjecture ; 1.1 Introduction; 1.2 The classical pictures; 1.2.1 The vanishing cycles formalism in étale cohomology; 1.2.2 The Rapoport-Zink construction; 1.2.3 The limit of a variation of Hodge structures; 1.2.4 The analogy between the situations in étale cohomology and Hodge theory; 1.3 Specialization systems; 1.3.1 The motivic categories. |
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1.3.2 Definitions and examples1.3.3 The basic results; 1.4 Constructing the vanishing cycles formalism; 1.4.1 The idea of the construction; 1.4.2 The cosimplicial motive A and the construction of Y; 1.4.3 The construction of \; 1.4.4 Pseudo-monoidal structure; 1.4.5 Compatibility with duality; 1.4.6 The monodromy operator; 1.5 Conservation conjecture. Application to Schur finiteness of motives; 1.5.1 The statement of the conjecture; 1.5.2 About the Schur finiteness of motives; 1.5.3 The conservation conjecture implies the Schur finiteness of motives. |
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1.5.4 Some steps toward the Conservation conjecture2 On the Theory of 1-Motives ; 2.1 On Picard Functors; 2.1.1 Simplicial Picard Functors; 2.1.2 Relative Picard Functors; 2.1.3 Higher Picard Functors; 2.2 On 1-Motives; 2.2.1 Generalities; 2.2.2 Hodge Realization; 2.2.3 Flat, ℓ-adic and Étale Realizations; 2.2.4 Crystalline Realization; 2.2.5 De Rham Realization; 2.2.6 Paradigma; 2.2.7 Cartier Duality; 2.2.8 Symmetric Avatar; 2.2.9 1-Motives with Torsion; 2.2.10 1-Motives up to Isogenies; 2.2.11 Universal Realization and Triangulated 1-Motives. |
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2.2.12 1-Motives with Additive Factors2.3 On 1-Motivic (Co)homology; 2.3.1 Albanese and Picard 1-Motives; 2.3.2 Hodge 1-Motives; 2.3.3 Non-homotopical Invariant Theories; 2.3.4 Final Remarks; 3 Motivic Decomposition for Resolutions of Threefolds ; 3.1 Introduction; 3.2 Intersection forms; 3.2.1 Surfaces; 3.2.2 Intersection forms associated to a map; 3.2.3 Resolutions of isolated singularities in dimension 3; 3.3 Intersection forms and Decomposition in the Derived Category; 3.3.1 Resolution of surface singularities. |
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3.3.2 Fibrations over curves3.3.3 Smooth maps; 3.4 Perverse sheaves and the Decomposition Theorem; 3.4.1 Truncation and Perverse sheaves; 3.4.2 The simple objects of P(Y ); 3.4.4 The Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber; 3.4.5 Results on intersection forms; 3.4.6 The decomposition mechanism; 3.5 Grothendieck motive decomposition for maps of threefolds; 4 Correspondences and Transfers ; 4.1 Finite Correspondences; 4.1.1 Relative Cycles; 4.1.2 Composition of Finite Correspondences; 4.1.3 Monoidal Structure. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Algebraic cycles -- Congresses.
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Algebraic cycles. |
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Motives (Mathematics) -- Congresses.
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Motives (Mathematics) |
| Genre/Form |
Electronic books.
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Conference papers and proceedings.
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Conference papers and proceedings.
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Festschriften.
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Festschriften.
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| Added Author |
Nagel, Jan.
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Peters, C. (Chris)
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Murre, Jacob P., 1929-
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European Algebraic Geometry Research Training Network.
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| Other Form: |
Print version: 9780521701747 |
| ISBN |
9781107362987 (electronic book) |
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1107362989 (electronic book) |
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9780511893926 (electronic book) |
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0511893922 (electronic book) |
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9780511721496 (ebook) |
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0511721498 (ebook) |
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0521701740 (paperback) |
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9780521701747 (paperback) |
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9780521701747 (paperback) |
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