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Algebraic cycles and motives. Volume 1 /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor Corporativo: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2007.
|
| Colección: | London Mathematical Society lecture note series ;
343. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 0 | 0 | |a Algebraic cycles and motives. |n Volume 1 / |c edited by Jan Nagel, Chris Peters. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2007. | ||
| 300 | |a 1 online resource (xiv, 292 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series ; |v 343 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Algebraic cycles |v Congresses. | |
| 650 | 0 | |a Motives (Mathematics) |v Congresses. | |
| 650 | 6 | |a Cycles algébriques |v Congrès. | |
| 650 | 6 | |a Motifs (Mathématiques) |v Congrès. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Algebraic cycles. |2 fast |0 (OCoLC)fst00804930 | |
| 650 | 7 | |a Motives (Mathematics) |2 fast |0 (OCoLC)fst01027555 | |
| 655 | 7 | |a Conference papers and proceedings. |2 fast |0 (OCoLC)fst01423772 | |
| 700 | 1 | |a Nagel, Jan. | |
| 700 | 1 | |a Peters, C. |q (Chris) | |
| 700 | 1 | |a Murre, Jacob P., |d 1929- | |
| 710 | 2 | |a European Algebraic Geometry Research Training Network. | |
| 776 | 0 | 8 | |i Print version: |z 9780521701747 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 343. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552365 |z Texto completo |
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