Algebraic Cycles and Motives, Volume 1

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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.

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. These two volumes provide a self-contained account of this subject as it stands today. Twenty-two contributions from leading figures 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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2012
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	308
ISBN-13:	9780521701747
ISBN-10:	0521701740
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Redaktion:	Peters, Chris
Hersteller:	Cambridge University Press
Maße:	229 x 152 x 18 mm
Von/Mit:	Chris Peters
Erscheinungsdatum:	09.10.2012
Gewicht:	0,503 kg

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