Hodge Theory

MN-49

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths , Lê Dũng Tráng

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English

Princeton University Press
21 July 2014

Analytic topology

Series: Mathematical Notes

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.

By: Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, Lê Dũng Tráng
Imprint: Princeton University Press
Country of Publication: United States
Volume: 49
Dimensions: Height: 235mm, Width: 152mm, Spine: 41mm
Weight: 851g
ISBN: 9780691161341
ISBN 10: 0691161348
Series: Mathematical Notes
Pages: 608
Publication Date: 21 July 2014
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

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.

Reviews for Hodge Theory (MN-49)

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