Overview
This book provides a comprehensive and up-to-date introduction to Hodge theory--one of the central and most vibrant areas of contemporary mathematics--from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kahler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck's algebraic de Rham theorem.The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne's theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, Francois Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Le D?ng Trang, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
Full Product Details
Author: Eduardo Cattani ,
Fouad El Zein ,
Phillip A. Griffiths ,
Lê Dũng Tráng
Publisher: Princeton University Press
Imprint: Princeton University Press
Volume: 49
Dimensions:
Width: 15.20cm
, Height: 4.10cm
, Length: 23.50cm
Weight: 0.851kg
ISBN: 9780691161341
ISBN 10: 0691161348
Pages: 608
Publication Date: 21 July 2014
Audience:
College/higher education
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Language: English
Reviews
Charles and Schnell's chapter beautifully surveys the theory of absolute Hodge classes, giving in particular a complete proof of Deligne's theorem on absolute Hodge classes on abelian varieties... A welcome addition to the literature and should be useful to both graduate students and researchers working in Hodge theory. --Dan Petersen, MathSciNet
Charles and Schnell's chapter beautifully surveys the theory of absolute Hodge classes, giving in particular a complete proof of Deligne's theorem on absolute Hodge classes on abelian varieties. . . . A welcome addition to the literature and should be useful to both graduate students and researchers working in Hodge theory. --Dan Petersen, MathSciNet
Author Information
Eduardo Cattani is professor of mathematics at the University of Massachusetts, Amherst. Fouad El Zein is a researcher at the Institut de Mathmatiques de Jussieu, Universit de Paris VII. Phillip A. Griffiths is former director and professor emeritus of mathematics at the Institute for Advanced Study in Princeton. L Dng Trng is professor emeritus of mathematics at the Aix-Marseille Universit.
