On the Tangent :: space to the space of algebraic cycles on a smooth algebraic variety /
In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
2004.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 157. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angéniol and Lejeune-Jalabert. The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications. |
| Beschreibung: | 1 online resource (vi, 200 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 195-197) and index. |
| ISBN: | 9780691120430 0691120439 9781400837175 1400837170 |
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| 245 | 1 | 0 | |a On the Tangent : |b space to the space of algebraic cycles on a smooth algebraic variety / |c Mark Green and Phillip Griffiths. |
| 260 | |a Princeton : |b Princeton University Press, |c 2004. | ||
| 300 | |a 1 online resource (vi, 200 pages) : |b illustrations | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 157 | |
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 195-197) and index. | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Abstract -- |t Chapter One. Introduction -- |t Chapter Two. The Classical Case When n 1 -- |t Chapter Three. Differential Geometry of Symmetric Products -- |t Chapter Four. Absolute Differentials (I) -- |t Chapter Five Geometric Description of T̳Z -- |t Chapter Six. Absolute Differentials (II) -- |t Chapter Seven. The Ext-definition of TZ -- |t Chapter Eight. Tangents to Related Spaces -- |t Chapter Nine. Applications and Examples -- |t Chapter Ten. Speculations and Questions -- |t Bibliography -- |t Index. |
| 520 | |a In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angéniol and Lejeune-Jalabert. The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications. | ||
| 546 | |a In English. | ||
| 650 | 0 | |a Algebraic cycles. |0 http://id.loc.gov/authorities/subjects/sh85035063 | |
| 650 | 0 | |a Geometry, Algebraic. |0 http://id.loc.gov/authorities/subjects/sh85054140 | |
| 650 | 0 | |a Hodge theory. |0 http://id.loc.gov/authorities/subjects/sh85061345 | |
| 650 | 6 | |a Cycles algébriques. | |
| 650 | 6 | |a Théorie de Hodge. | |
| 650 | 6 | |a Géométrie algébrique. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Abstract. |2 bisacsh | |
| 650 | 7 | |a Algebraic cycles |2 fast | |
| 650 | 7 | |a Geometry, Algebraic |2 fast | |
| 650 | 7 | |a Hodge theory |2 fast | |
| 758 | |i has work: |a On the Tangent (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH4tJVJH9THCJ896X8hwkC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t On the Tangent. |d Princeton : Princeton University Press, 2004 |w (OCoLC)56759558 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 157. |0 http://id.loc.gov/authorities/names/n42002129 | |
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Datensatz im Suchindex
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| adam_text | |
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| author | Green, M. (Mark) |
| author_GND | http://id.loc.gov/authorities/names/n94097484 |
| author_facet | Green, M. (Mark) |
| author_role | |
| author_sort | Green, M. |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
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| contents | Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Z -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index. |
| ctrlnum | (OCoLC)779498413 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
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| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn779498413 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:17Z |
| institution | BVB |
| isbn | 9780691120430 0691120439 9781400837175 1400837170 |
| language | English |
| oclc_num | 779498413 |
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| physical | 1 online resource (vi, 200 pages) : illustrations |
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| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Princeton University Press, |
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| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Green, M. (Mark) https://id.oclc.org/worldcat/entity/E39PBJghp6vMBBxydRqbtMGrbd http://id.loc.gov/authorities/names/n94097484 On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / Mark Green and Phillip Griffiths. Princeton : Princeton University Press, 2004. 1 online resource (vi, 200 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Annals of mathematics studies ; no. 157 Print version record. Includes bibliographical references (pages 195-197) and index. Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Z -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index. In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angéniol and Lejeune-Jalabert. The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications. In English. Algebraic cycles. http://id.loc.gov/authorities/subjects/sh85035063 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Hodge theory. http://id.loc.gov/authorities/subjects/sh85061345 Cycles algébriques. Théorie de Hodge. Géométrie algébrique. MATHEMATICS Geometry Algebraic. bisacsh MATHEMATICS Algebra Abstract. bisacsh Algebraic cycles fast Geometry, Algebraic fast Hodge theory fast has work: On the Tangent (Text) https://id.oclc.org/worldcat/entity/E39PCH4tJVJH9THCJ896X8hwkC https://id.oclc.org/worldcat/ontology/hasWork Print version: On the Tangent. Princeton : Princeton University Press, 2004 (OCoLC)56759558 Annals of mathematics studies ; no. 157. http://id.loc.gov/authorities/names/n42002129 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=536885 Volltext |
| spellingShingle | Green, M. (Mark) On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / Annals of mathematics studies ; Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Z -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index. Algebraic cycles. http://id.loc.gov/authorities/subjects/sh85035063 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Hodge theory. http://id.loc.gov/authorities/subjects/sh85061345 Cycles algébriques. Théorie de Hodge. Géométrie algébrique. MATHEMATICS Geometry Algebraic. bisacsh MATHEMATICS Algebra Abstract. bisacsh Algebraic cycles fast Geometry, Algebraic fast Hodge theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85035063 http://id.loc.gov/authorities/subjects/sh85054140 http://id.loc.gov/authorities/subjects/sh85061345 |
| title | On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / |
| title_alt | Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Z -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index. |
| title_auth | On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / |
| title_exact_search | On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / |
| title_full | On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / Mark Green and Phillip Griffiths. |
| title_fullStr | On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / Mark Green and Phillip Griffiths. |
| title_full_unstemmed | On the Tangent : space to the space of algebraic cycles on a smooth algebraic variety / Mark Green and Phillip Griffiths. |
| title_short | On the Tangent : |
| title_sort | on the tangent space to the space of algebraic cycles on a smooth algebraic variety |
| title_sub | space to the space of algebraic cycles on a smooth algebraic variety / |
| topic | Algebraic cycles. http://id.loc.gov/authorities/subjects/sh85035063 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Hodge theory. http://id.loc.gov/authorities/subjects/sh85061345 Cycles algébriques. Théorie de Hodge. Géométrie algébrique. MATHEMATICS Geometry Algebraic. bisacsh MATHEMATICS Algebra Abstract. bisacsh Algebraic cycles fast Geometry, Algebraic fast Hodge theory fast |
| topic_facet | Algebraic cycles. Geometry, Algebraic. Hodge theory. Cycles algébriques. Théorie de Hodge. Géométrie algébrique. MATHEMATICS Geometry Algebraic. MATHEMATICS Algebra Abstract. Algebraic cycles Geometry, Algebraic Hodge theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=536885 |
| work_keys_str_mv | AT greenm onthetangentspacetothespaceofalgebraiccyclesonasmoothalgebraicvariety |