The Gross-Zagier formula on Shimura curves /:
This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations....
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
2012, ©2013.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 184. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. |
| Beschreibung: | 1 online resource (viii, 256 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781400845644 1400845645 0691155925 9780691155920 0691155917 9780691155913 |
Internformat
MARC
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| 100 | 1 | |a Yuan, Xinyi, |d 1981- | |
| 245 | 1 | 4 | |a The Gross-Zagier formula on Shimura curves / |c Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. |
| 260 | |a Princeton : |b Princeton University Press, |c 2012, ©2013. | ||
| 300 | |a 1 online resource (viii, 256 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 184 | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Chapter One. Introduction and Statement of Main Results -- |t Chapter Two. Weil Representation and Waldspurger Formula -- |t Chapter Three. Mordell-Weil Groups and Generating Series -- |t Chapter Four. Trace of the Generating Series -- |t Chapter Five. Assumptions on the Schwartz Function -- |t Chapter Six. Derivative of the Analytic Kernel -- |t Chapter Seven. Decomposition of the Geometric Kernel -- |t Chapter Eight. Local Heights of CM Points -- |t Bibliography -- |t Index. |
| 546 | |a In English. | ||
| 650 | 0 | |a Shimura varieties. |0 http://id.loc.gov/authorities/subjects/sh93007485 | |
| 650 | 0 | |a Arithmetical algebraic geometry. |0 http://id.loc.gov/authorities/subjects/sh87002041 | |
| 650 | 0 | |a Automorphic forms. |0 http://id.loc.gov/authorities/subjects/sh85010451 | |
| 650 | 0 | |a Quaternions. |0 http://id.loc.gov/authorities/subjects/sh85109754 | |
| 650 | 6 | |a Variétés de Shimura. | |
| 650 | 6 | |a Géométrie algébrique arithmétique. | |
| 650 | 6 | |a Formes automorphes. | |
| 650 | 6 | |a Quaternions. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Arithmetical algebraic geometry |2 fast | |
| 650 | 7 | |a Automorphic forms |2 fast | |
| 650 | 7 | |a Quaternions |2 fast | |
| 650 | 7 | |a Shimura varieties |2 fast | |
| 700 | 1 | |a Zhang, Shouwu. | |
| 700 | 1 | |a Zhang, Wei, |d 1981- | |
| 776 | 0 | 8 | |i Print version: |a Yuan, Xinyi, 1981- |t Gross-Zagier formula on Shimura curves. |d Princeton : Princeton University Press, 2012, ©2013 |w (DLC) 2012010981 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 184. | |
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Datensatz im Suchindex
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| _version_ | 1816882208549371904 |
| adam_text | |
| any_adam_object | |
| author | Yuan, Xinyi, 1981- |
| author2 | Zhang, Shouwu Zhang, Wei, 1981- |
| author2_role | |
| author2_variant | s z sz w z wz |
| author_facet | Yuan, Xinyi, 1981- Zhang, Shouwu Zhang, Wei, 1981- |
| author_role | |
| author_sort | Yuan, Xinyi, 1981- |
| author_variant | x y xy |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA242 |
| callnumber-raw | QA242.5 .Y83 2012eb |
| callnumber-search | QA242.5 .Y83 2012eb |
| callnumber-sort | QA 3242.5 Y83 42012EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index. |
| ctrlnum | (OCoLC)811400574 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn811400574 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:24:57Z |
| institution | BVB |
| isbn | 9781400845644 1400845645 0691155925 9780691155920 0691155917 9780691155913 |
| language | English |
| oclc_num | 811400574 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (viii, 256 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Princeton University Press, |
| record_format | marc |
| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Yuan, Xinyi, 1981- The Gross-Zagier formula on Shimura curves / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. Princeton : Princeton University Press, 2012, ©2013. 1 online resource (viii, 256 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Annals of mathematics studies ; no. 184 Includes bibliographical references and index. This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index. In English. Shimura varieties. http://id.loc.gov/authorities/subjects/sh93007485 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Variétés de Shimura. Géométrie algébrique arithmétique. Formes automorphes. Quaternions. MATHEMATICS Geometry Algebraic. bisacsh Arithmetical algebraic geometry fast Automorphic forms fast Quaternions fast Shimura varieties fast Zhang, Shouwu. Zhang, Wei, 1981- Print version: Yuan, Xinyi, 1981- Gross-Zagier formula on Shimura curves. Princeton : Princeton University Press, 2012, ©2013 (DLC) 2012010981 Annals of mathematics studies ; no. 184. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=479005 Volltext |
| spellingShingle | Yuan, Xinyi, 1981- The Gross-Zagier formula on Shimura curves / Annals of mathematics studies ; Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index. Shimura varieties. http://id.loc.gov/authorities/subjects/sh93007485 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Variétés de Shimura. Géométrie algébrique arithmétique. Formes automorphes. Quaternions. MATHEMATICS Geometry Algebraic. bisacsh Arithmetical algebraic geometry fast Automorphic forms fast Quaternions fast Shimura varieties fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh93007485 http://id.loc.gov/authorities/subjects/sh87002041 http://id.loc.gov/authorities/subjects/sh85010451 http://id.loc.gov/authorities/subjects/sh85109754 |
| title | The Gross-Zagier formula on Shimura curves / |
| title_alt | Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index. |
| title_auth | The Gross-Zagier formula on Shimura curves / |
| title_exact_search | The Gross-Zagier formula on Shimura curves / |
| title_full | The Gross-Zagier formula on Shimura curves / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. |
| title_fullStr | The Gross-Zagier formula on Shimura curves / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. |
| title_full_unstemmed | The Gross-Zagier formula on Shimura curves / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. |
| title_short | The Gross-Zagier formula on Shimura curves / |
| title_sort | gross zagier formula on shimura curves |
| topic | Shimura varieties. http://id.loc.gov/authorities/subjects/sh93007485 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Variétés de Shimura. Géométrie algébrique arithmétique. Formes automorphes. Quaternions. MATHEMATICS Geometry Algebraic. bisacsh Arithmetical algebraic geometry fast Automorphic forms fast Quaternions fast Shimura varieties fast |
| topic_facet | Shimura varieties. Arithmetical algebraic geometry. Automorphic forms. Quaternions. Variétés de Shimura. Géométrie algébrique arithmétique. Formes automorphes. MATHEMATICS Geometry Algebraic. Arithmetical algebraic geometry Automorphic forms Quaternions Shimura varieties |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=479005 |
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