Hodge Theory (MN-49) / / Eduardo Cattani, Lê Dũng Tráng, Phillip A. Griffiths, Fouad El Zein.
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 stru...
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Year of Publication: | 2014 |
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Cattani, Eduardo, author. aut http://id.loc.gov/vocabulary/relators/aut Hodge Theory (MN-49) / Eduardo Cattani, Lê Dũng Tráng, Phillip A. Griffiths, Fouad El Zein. Course Book Princeton, NJ : Princeton University Press, [2014] ©2014 1 online resource (608 p.) : 10 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Notes ; 49 Frontmatter -- Contributors -- Contents -- Preface -- Chapter One. Introduction to Kähler Manifolds -- Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem -- Chapter Three. Mixed Hodge Structures -- Chapter Four. Period Domains and Period Mappings -- Chapter Five. The Hodge Theory of Maps -- Chapter Six The Hodge Theory of Maps -- Chapter Seven. Introduction to Variations of Hodge Structure -- Chapter Eight. Variations of Mixed Hodge Structure -- Chapter Nine. Lectures on Algebraic Cycles and Chow Groups -- Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles -- Chapter Eleven. Notes on Absolute Hodge Classes -- Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Hodge theory. Manifolds (Mathematics) Congresses. MATHEMATICS / Topology. bisacsh 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-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. Brosnan, Patrick, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Carlson, James, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Cataldo, Mark Andrea de, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Cattani, Eduardo, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Charles, François, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb El Zein, Fouad, author. aut http://id.loc.gov/vocabulary/relators/aut El Zein, Fouad, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Green, Mark L., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Griffiths, Phillip A., author. aut http://id.loc.gov/vocabulary/relators/aut Kerr, Matt, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Migliorini, Luca, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Murre, Jacob, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Schnell, Christian, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Tráng, Lê Dũng, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Tu, Loring W., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Zein, Fouad El, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 9783110494921 ZDB-23-PMN Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 print 9780691161341 https://doi.org/10.1515/9781400851478 https://www.degruyter.com/isbn/9781400851478 Cover https://www.degruyter.com/document/cover/isbn/9781400851478/original |
language |
English |
format |
eBook |
author |
Cattani, Eduardo, Cattani, Eduardo, El Zein, Fouad, Griffiths, Phillip A., |
spellingShingle |
Cattani, Eduardo, Cattani, Eduardo, El Zein, Fouad, Griffiths, Phillip A., Hodge Theory (MN-49) / Mathematical Notes ; Frontmatter -- Contributors -- Contents -- Preface -- Chapter One. Introduction to Kähler Manifolds -- Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem -- Chapter Three. Mixed Hodge Structures -- Chapter Four. Period Domains and Period Mappings -- Chapter Five. The Hodge Theory of Maps -- Chapter Six The Hodge Theory of Maps -- Chapter Seven. Introduction to Variations of Hodge Structure -- Chapter Eight. Variations of Mixed Hodge Structure -- Chapter Nine. Lectures on Algebraic Cycles and Chow Groups -- Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles -- Chapter Eleven. Notes on Absolute Hodge Classes -- Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective -- Bibliography -- Index |
author_facet |
Cattani, Eduardo, Cattani, Eduardo, El Zein, Fouad, Griffiths, Phillip A., Brosnan, Patrick, Brosnan, Patrick, Carlson, James, Carlson, James, Cataldo, Mark Andrea de, Cataldo, Mark Andrea de, Cattani, Eduardo, Cattani, Eduardo, Charles, François, Charles, François, El Zein, Fouad, El Zein, Fouad, El Zein, Fouad, El Zein, Fouad, Green, Mark L., Green, Mark L., Griffiths, Phillip A., Griffiths, Phillip A., Kerr, Matt, Kerr, Matt, Migliorini, Luca, Migliorini, Luca, Murre, Jacob, Murre, Jacob, Schnell, Christian, Schnell, Christian, Tráng, Lê Dũng, Tráng, Lê Dũng, Tu, Loring W., Tu, Loring W., Zein, Fouad El, Zein, Fouad El, |
author_variant |
e c ec e c ec z f e zf zfe p a g pa pag |
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VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Brosnan, Patrick, Brosnan, Patrick, Carlson, James, Carlson, James, Cataldo, Mark Andrea de, Cataldo, Mark Andrea de, Cattani, Eduardo, Cattani, Eduardo, Charles, François, Charles, François, El Zein, Fouad, El Zein, Fouad, El Zein, Fouad, El Zein, Fouad, Green, Mark L., Green, Mark L., Griffiths, Phillip A., Griffiths, Phillip A., Kerr, Matt, Kerr, Matt, Migliorini, Luca, Migliorini, Luca, Murre, Jacob, Murre, Jacob, Schnell, Christian, Schnell, Christian, Tráng, Lê Dũng, Tráng, Lê Dũng, Tu, Loring W., Tu, Loring W., Zein, Fouad El, Zein, Fouad El, |
author2_variant |
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author_sort |
Cattani, Eduardo, |
title |
Hodge Theory (MN-49) / |
title_full |
Hodge Theory (MN-49) / Eduardo Cattani, Lê Dũng Tráng, Phillip A. Griffiths, Fouad El Zein. |
title_fullStr |
Hodge Theory (MN-49) / Eduardo Cattani, Lê Dũng Tráng, Phillip A. Griffiths, Fouad El Zein. |
title_full_unstemmed |
Hodge Theory (MN-49) / Eduardo Cattani, Lê Dũng Tráng, Phillip A. Griffiths, Fouad El Zein. |
title_auth |
Hodge Theory (MN-49) / |
title_alt |
Frontmatter -- Contributors -- Contents -- Preface -- Chapter One. Introduction to Kähler Manifolds -- Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem -- Chapter Three. Mixed Hodge Structures -- Chapter Four. Period Domains and Period Mappings -- Chapter Five. The Hodge Theory of Maps -- Chapter Six The Hodge Theory of Maps -- Chapter Seven. Introduction to Variations of Hodge Structure -- Chapter Eight. Variations of Mixed Hodge Structure -- Chapter Nine. Lectures on Algebraic Cycles and Chow Groups -- Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles -- Chapter Eleven. Notes on Absolute Hodge Classes -- Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective -- Bibliography -- Index |
title_new |
Hodge Theory (MN-49) / |
title_sort |
hodge theory (mn-49) / |
series |
Mathematical Notes ; |
series2 |
Mathematical Notes ; |
publisher |
Princeton University Press, |
publishDate |
2014 |
physical |
1 online resource (608 p.) : 10 line illus. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contributors -- Contents -- Preface -- Chapter One. Introduction to Kähler Manifolds -- Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem -- Chapter Three. Mixed Hodge Structures -- Chapter Four. Period Domains and Period Mappings -- Chapter Five. The Hodge Theory of Maps -- Chapter Six The Hodge Theory of Maps -- Chapter Seven. Introduction to Variations of Hodge Structure -- Chapter Eight. Variations of Mixed Hodge Structure -- Chapter Nine. Lectures on Algebraic Cycles and Chow Groups -- Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles -- Chapter Eleven. Notes on Absolute Hodge Classes -- Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective -- Bibliography -- Index |
isbn |
9781400851478 9783110494921 9783110665925 9780691161341 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA564 |
callnumber-sort |
QA 3564 S88 42017 |
url |
https://doi.org/10.1515/9781400851478 https://www.degruyter.com/isbn/9781400851478 https://www.degruyter.com/document/cover/isbn/9781400851478/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514.74 |
dewey-sort |
3514.74 |
dewey-raw |
514.74 |
dewey-search |
514.74 |
doi_str_mv |
10.1515/9781400851478 |
oclc_num |
882259923 |
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