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nagel jan (curatore); peters chris (curatore) - algebraic cycles and motives: volume 1

Algebraic Cycles and Motives: Volume 1

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Genere:Libro
Lingua: Inglese
Pubblicazione: 05/2007





Trama

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.




Sommario

Foreword; Part I. Survey Articles: 1. The motivic vanishing cycles and the conservation conjecture J. Ayoub; 2. On the theory of 1-motives L. Barbieri-Viale; 3. Motivic decomposition for resolutions of threefolds M. de Cataldo and L. Migliorini; 4. Correspondences and transfers F. D´eglise; 5. Algebraic cycles and singularities of normal functions M. Green and Ph. Griffiths; 6. Zero cycles on singular varieties A. Krishna and V. Srinivas; 7. Modular curves, modular surfaces and modular fourfolds D. Ramakrishnan.




Prefazione

These two volumes provide a self-contained account of research on algebraic cycles and motives. Twenty-two contributions from leading figures survey the key research strands, including: Abel-Jacobi/regulator maps and normal functions; Voevodsky's triangulated category of mixed motives; conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups.




Autore

Jan Nagel is a Lecturer at UFR de Mathématiques Pures et Appliquées, Université Lille 1.
Chris Peters is a Professor at Institut Fourier, Université Grenoble 1.










Altre Informazioni

ISBN:

9780521701747

Condizione: Nuovo
Collana: London Mathematical Society Lecture Note Series
Dimensioni: 229 x 18 x 152 mm Ø 514 gr
Formato: Brossura
Illustration Notes:8 b/w illus.
Pagine Arabe: 308


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