Hodge Theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, N.J.
Princeton University Press
[2014]
|
| Series: | Mathematical Notes
49 |
| Subjects: | |
| Online Access: | DE-91 Volltext |
| Physical Description: | 608p. |
| ISBN: | 9781400851478 9781306783668 |
| DOI: | 10.1515/9781400851478 |
Staff View
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| 505 | 8 | |a 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 D?ng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu | |
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| contents | 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 D?ng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu |
| ctrlnum | (OCoLC)882259923 (DE-599)BVBBV042523194 |
| dewey-full | 514.223 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.223 |
| dewey-search | 514.223 |
| dewey-sort | 3514.223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400851478 |
| format | Electronic eBook |
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| id | DE-604.BV042523194 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-19T17:41:08Z |
| institution | BVB |
| isbn | 9781400851478 9781306783668 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027957533 |
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| physical | 608p. |
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| publishDate | 2014 |
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| publisher | Princeton University Press |
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| series | Mathematical Notes |
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| spelling | Lê, Dũng Tráng 1947- Verfasser (DE-588)138156530 aut Hodge Theory Lê Dung Tráng, Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths Princeton, N.J. Princeton University Press [2014] 608p. txt rdacontent c rdamedia cr rdacarrier Online-Ressource Mathematical Notes 49 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 D?ng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu In English Mathematik Manifolds (Mathematics) / Congresses Hodge-Theorie (DE-588)4135967-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Hodge-Theorie (DE-588)4135967-7 s DE-604 Cattani, Eduardo Sonstige oth El Zein, Fouad Sonstige oth Griffiths, Phillip 1938- Sonstige (DE-588)131881434 oth Erscheint auch als Druck-Ausgabe 978-0-691-16134-1 Mathematical Notes 49 (DE-604)BV013563374 49 https://doi.org/10.1515/9781400851478 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Lê, Dũng Tráng 1947- Hodge Theory 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 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 D?ng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu Mathematik Manifolds (Mathematics) / Congresses Hodge-Theorie (DE-588)4135967-7 gnd |
| subject_GND | (DE-588)4135967-7 (DE-588)1071861417 |
| title | Hodge Theory |
| title_auth | Hodge Theory |
| title_exact_search | Hodge Theory |
| title_full | Hodge Theory Lê Dung Tráng, Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths |
| title_fullStr | Hodge Theory Lê Dung Tráng, Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths |
| title_full_unstemmed | Hodge Theory Lê Dung Tráng, Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths |
| title_short | Hodge Theory |
| title_sort | hodge theory |
| topic | Mathematik Manifolds (Mathematics) / Congresses Hodge-Theorie (DE-588)4135967-7 gnd |
| topic_facet | Mathematik Manifolds (Mathematics) / Congresses Hodge-Theorie Konferenzschrift |
| url | https://doi.org/10.1515/9781400851478 |
| volume_link | (DE-604)BV013563374 |
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