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Chow rings, decomposition of the diagonal, and the topology of families /
In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2014.
|
| Colección: | Annals of mathematics studies ;
no. 187. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Voisin, Claire, |d 1962- |e author. | |
| 245 | 1 | 0 | |a Chow rings, decomposition of the diagonal, and the topology of families / |c Claire Voisin. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2014. | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (viii, 162 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file | ||
| 347 | |b PDF | ||
| 490 | 1 | |a Annals of mathematics studies ; |v number 187 | |
| 504 | |a Includes bibliographical references (pages 155-162) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Chapter One. Introduction -- |t Chapter Two. Review of Hodge theory and algebraic cycles -- |t Chapter Three. Decomposition of the diagonal -- |t Chapter Four. Chow groups of large coniveau complete intersections -- |t Chapter Five. On the Chow ring of K3 surfaces and hyper-Kähler manifolds -- |t Chapter Six. Integral coefficients -- |t Bibliography -- |t Index. |
| 546 | |a In English. | ||
| 520 | |a In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by Voisin. The book focuses on two central objects: the diagonal of a variety--and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups--as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by Voisin looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 650 | 0 | |a Algebraic varieties. | |
| 650 | 0 | |a Decomposition (Mathematics) | |
| 650 | 0 | |a Homology theory. | |
| 650 | 6 | |a Variétés algébriques. | |
| 650 | 6 | |a Décomposition (Mathématiques) | |
| 650 | 6 | |a Homologie. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Algebraic varieties |2 fast | |
| 650 | 7 | |a Decomposition (Mathematics) |2 fast | |
| 650 | 7 | |a Homology theory |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Voisin, Claire, 1962- |t Chow rings, decomposition of the diagonal, and the topology of families. |d Princeton : Princeton University Press, [2013] |z 9780691160504 |w (DLC) 2013016992 |w (OCoLC)852745692 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 187. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt5hhp7w |z Texto completo |
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