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  • 1
    Book
    Book
    Lectures on the arithmetic Riemann-Roch theorem / (1992)
    Princeton, New Jersey :Princeton University Press,
    Details
    UID:
    almahu_BV006135105
    Format: X, 100 Seiten.
    ISBN: 0-691-08771-7 , 0-691-02544-4 , 978-0-691-02544-5
    Series Statement: Annals of Mathematics Studies number 127
    Additional Edition: Elektronische Reproduktion ISBN 9781400882472
    Language: English
    Subjects: Mathematics
    RVK:
    SI 830
    RVK:
    SK 240
    Keywords: Riemann-Roch-Satz ; Algebraische Geometrie ; Algebraische Geometrie
    URL: Inhaltsverzeichnis
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
    URL: Inhaltsverzeichnis
    Author information: Faltings, Gerd, 1954-,
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  • 2
    Online Resource
    Online Resource
    Heegner points and Rankin L-series / (2004)
    Cambridge :Cambridge University Press,
    Details
    UID:
    almahu_9948233629602882
    Format: 1 online resource (xiii, 367 pages) : , digital, PDF file(s).
    ISBN: 9780511756375 (ebook)
    Series Statement: Mathematical Sciences Research Institute publications ; 49
    Content: The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin L-series has led to many generalisations and extensions in a variety of different directions, spawning a fertile area of study that remains active to this day. This volume, based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, is a collection of thirteen articles written by many of the leading contributors in the field, having the Gross-Zagier formula and its avatars as a common unifying theme. It serves as a valuable reference for mathematicians wishing to become further acquainted with the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
    Additional Edition: Print version: ISBN 9780521836593
    Language: English
    Subjects: Mathematics
    RVK:
    SK 180
    URL: https://doi.org/10.1017/CBO9780511756375
    URL: Volltext
    URL: Inhaltstext
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    Online Access
    HU Berlin
    FU Berlin
    UB Potsdam
  • 3
    Book
    Book
    The Gross-Zagier formula on Shimura curves / (2013)
    Princeton ; Oxford :Princeton University Press,
    Details
    UID:
    almahu_BV040724442
    Format: viii, 256 Seiten ; , 25 cm.
    ISBN: 978-0-691-15591-3 , 978-0-691-15592-0
    Series Statement: Annals of mathematics studies number 184
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 9781400845644
    Language: English
    Subjects: Mathematics
    RVK:
    SI 830
    RVK:
    SK 370
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
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  • 4
    Online Resource
    Online Resource
    The Gross-Zagier formula on Shimura curves (2013)
    Princeton, N.J. : Princeton University Press
    Details
    UID:
    b3kat_BV042523080
    Format: 1 Online-Ressource (272 S.)
    ISBN: 9781400845644
    Series Statement: Annals of Mathematics Studies number 184
    Note: Biographical note: Xinyi Yuan is assistant professor of mathematics at Princeton University. Shou-wu Zhang is professor of mathematics at Princeton University and Columbia University. Wei Zhang is assistant professor of mathematics at Columbia University , Main description: 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. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-0-691-15591-3
    Language: English
    Subjects: Mathematics
    RVK:
    SI 830
    RVK:
    SK 370
    DOI: 10.1515/9781400845644
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext
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    Online Resource
    Online Access
    Open Access Request
    TU Berlin
  • 5
    Online Resource
    Online Resource
    Heegner points and Rankin L-series (2004)
    Cambridge, UK ; : Cambridge University Press,
    Details
    UID:
    almahu_9948310971302882
    Format: xiii, 367 p.
    Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.
    Series Statement: Mathematical Sciences Research Institute publications ; 49
    Language: English
    Keywords: Electronic books.
    URL: Click to View
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    HU Berlin
  • 6
    Online Resource
    Online Resource
    The Gross-Zagier formula on Shimura curves (2012)
    Princeton :Princeton University Press,
    Details
    UID:
    almahu_9948316089302882
    Format: viii, 256 p.
    Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.
    Series Statement: Annals of mathematics studies ; no. 184
    Language: English
    Keywords: Electronic books.
    URL: Click to View
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    HU Berlin
  • 7
    Online Resource
    Online Resource
    The Gross-Zagier formula on Shimura curves / (2012)
    Princeton :Princeton University Press,
    Details
    UID:
    edocfu_9959229099602883
    Format: 1 online resource (267 p.)
    Edition: Course Book
    ISBN: 9786613883919 , 1-4008-4564-5 , 1-283-57146-3
    Series Statement: Annals of mathematics studies ; no. 184
    Content: 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. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.
    Note: Description based upon print version of record. , 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 , Issued also in print. , English
    Additional Edition: ISBN 0-691-15592-5
    Additional Edition: ISBN 0-691-15591-7
    Language: English
    DOI: 10.1515/9781400845644
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    FU Berlin
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