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Cover: 9780521701754 | Algebraic Cycles and Motives, Volume 2 | Chris Peters | Taschenbuch
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Algebraic Cycles and Motives, Volume 2
Taschenbuch von Chris Peters
Sprache: Englisch

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Beschreibung
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 book is one of two volumes that provide a self-contained account of the subject as it stands today. 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.
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 book is one of two volumes that provide a self-contained account of the subject as it stands today. 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.
Zusammenfassung
Algebraic cycles and motives is a subfield of pure mathematics which has attracted much attention since the pioneering work of A. Grothendieck on motives. This two volume book presents twenty-two selected papers from the international EAGER conference 'Algebraic Cycles and Motives'. Both survey and research articles are included, covering the main research topics and interesting new results. Topics discussed include the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives; the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture.
Inhaltsverzeichnis
Part II. Research Articles: 8. Beilinson's Hodge conjecture with coefficients M. Asakura and S. Saito; 9. On the splitting of the Bloch-Beilinson filtration A. Beauville; 10. Künneth projectors S. Bloch and H. Esnault; 11. The Brill-Noether curve of a stable bundle on a genus two curve S. Brivio and A. Verra; 12. On Tannaka duality for vector bundles on p-adic curves C. Deninger and A. Werner; 13. On finite-dimensional motives and Murre's conjecture U. Jannsen; 14. On the transcendental part of the motive of a surface B. Kahn, J. P. Murre and C. Pedrini; 15. A note on finite dimensional motives S. I. Kimura; 16. Real regulators on Milnor complexes, II J. D. Lewis; 17. Motives for Picard modular surfaces A. Miller, S. Müller-Stach, S. Wortmann, Y.-H.Yang, K. Zuo; 18. The regulator map for complete intersections J. Nagel; 19. Hodge number polynomials for nearby and vanishing cohomology C. Peters and J. Steenbrink; 20. Direct image of logarithmic complexes M. Saito; 21. Mordell-Weil lattices of certain elliptic K3's T. Shioda; 22. Motives from diffraction J. Stienstra.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780521701754
ISBN-10: 0521701759
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Redaktion: Peters, Chris
Hersteller: Cambridge University Press
Maße: 229 x 152 x 22 mm
Von/Mit: Chris Peters
Erscheinungsdatum: 09.12.2010
Gewicht: 0,606 kg
Artikel-ID: 102105695
Zusammenfassung
Algebraic cycles and motives is a subfield of pure mathematics which has attracted much attention since the pioneering work of A. Grothendieck on motives. This two volume book presents twenty-two selected papers from the international EAGER conference 'Algebraic Cycles and Motives'. Both survey and research articles are included, covering the main research topics and interesting new results. Topics discussed include the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives; the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture.
Inhaltsverzeichnis
Part II. Research Articles: 8. Beilinson's Hodge conjecture with coefficients M. Asakura and S. Saito; 9. On the splitting of the Bloch-Beilinson filtration A. Beauville; 10. Künneth projectors S. Bloch and H. Esnault; 11. The Brill-Noether curve of a stable bundle on a genus two curve S. Brivio and A. Verra; 12. On Tannaka duality for vector bundles on p-adic curves C. Deninger and A. Werner; 13. On finite-dimensional motives and Murre's conjecture U. Jannsen; 14. On the transcendental part of the motive of a surface B. Kahn, J. P. Murre and C. Pedrini; 15. A note on finite dimensional motives S. I. Kimura; 16. Real regulators on Milnor complexes, II J. D. Lewis; 17. Motives for Picard modular surfaces A. Miller, S. Müller-Stach, S. Wortmann, Y.-H.Yang, K. Zuo; 18. The regulator map for complete intersections J. Nagel; 19. Hodge number polynomials for nearby and vanishing cohomology C. Peters and J. Steenbrink; 20. Direct image of logarithmic complexes M. Saito; 21. Mordell-Weil lattices of certain elliptic K3's T. Shioda; 22. Motives from diffraction J. Stienstra.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780521701754
ISBN-10: 0521701759
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Redaktion: Peters, Chris
Hersteller: Cambridge University Press
Maße: 229 x 152 x 22 mm
Von/Mit: Chris Peters
Erscheinungsdatum: 09.12.2010
Gewicht: 0,606 kg
Artikel-ID: 102105695
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