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Hodge theory / / edited by Eduardo Cattani [and three others] ; Patrick Brosnan [and thirteen others], contributors



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Autore: Cattani Eduardo Visualizza persona
Titolo: Hodge theory / / edited by Eduardo Cattani [and three others] ; Patrick Brosnan [and thirteen others], contributors Visualizza cluster
Pubblicazione: Princeton, New Jersey : , : Princeton University Press, , 2014
©2014
Edizione: Course Book
Descrizione fisica: 1 online resource (608 p.)
Disciplina: 514.223
Soggetto topico: Manifolds (Mathematics)
Soggetto non controllato: Abel–Jacobi map
Adélic lemmas
Albanese kernel
Bloch–Beilinson conjecture
Chow groups
Decomposition theorem
Deligne cohomology
Deligne's theorem
Galois action
Griffiths group
Griffiths' period map
Grothendieck's theorem
Hermitian structures
Hermitian symmetric domains
Hodge bundles
Hodge cycles
Hodge structure
Hodge structures
Hodge theory
Hodge-theoretic interpretations
Jacobian ideal
Kodaira–Spencer map
Kuga–Satake correspondence
Kähler manifolds
Kähler structures
Lefschetz decomposition
Poincaré residues
Schmid's orbit theorems
Shimura varieties
Thom–Whitney results
Torelli theorem
Verdier duality
absolute Hodge classes
abstract variations
algebraic cycles
algebraic equivalence
algebraic homology
algebraic maps
algebraic varieties
algebraicity
asymptotic behavior
coherent sheaves
cohomology
compact Kähler manifolds
complex manifolds
complex multiplication
conjectural filtration
contemporary mathematics
cycle class
cycle map
de Rham cohomology
de Rham theorem
differential forms
elliptic curves
equivalence relations
harmonic forms
holomorphicity
homological equivalence
horizontal distribution
horizontality
hypercohomology
hypersurfaces
intersection cohomology complex
intersection cohomology groups
invariant cycle theorem
linear algebra
local systems
mixed Hodge complex
mixed Hodge structure
mixed Hodge structures
monodromy
morphisms
nontrivial topological constraints
normal functions
period domains
period mappings
sheaf cohomology
smooth case
smooth projective varieties
spectral sequences
spread philosophy
spreads
symplectic structures
tangent space
topological invariants
variational Hodge conjecture
Čech cohomology
Classificazione: SI 850
Persona (resp. second.): CattaniEduardo
BrosnanPatrick
Note generali: "Between 14 June and 2 July 2010, the Summer School on Hodge Theory and Related Topics and a related conference were hosted by the ICTP in Trieste, Italy."
Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
Nota di contenuto: Front matter -- Contributors -- Contents -- Preface -- Chapter One. Introduction to Kähler Manifolds / Cattani, Eduardo -- Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem / El Zein, Fouad / Tu, Loring W. -- Chapter Three. Mixed Hodge Structures / Zein, Fouad El / Tráng, Lê Dũng -- Chapter Four. Period Domains and Period Mappings / Carlson, James -- Chapter Five. The Hodge Theory of Maps / Cataldo, Mark Andrea de / Migliorini, Luca -- Chapter Six The Hodge Theory of Maps / Cataldo, Mark Andrea de / Migliorini, Luca -- Chapter Seven. Introduction to Variations of Hodge Structure / Cattani, Eduardo -- Chapter Eight. Variations of Mixed Hodge Structure / Brosnan, Patrick / Zein, Fouad El -- Chapter Nine. Lectures on Algebraic Cycles and Chow Groups / Murre, Jacob -- Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles / Green, Mark L. -- Chapter Eleven. Notes on Absolute Hodge Classes / Charles, François / Schnell, Christian -- Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective / Kerr, Matt -- Bibliography -- Index
Sommario/riassunto: 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 Kähler 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, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
Titolo autorizzato: Hodge theory  Visualizza cluster
ISBN: 1-4008-5147-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910817118803321
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Serie: Mathematical notes (Princeton University Press) ; ; 49.