Author: Friedrich Hirzebruch
Publisher:
ISBN:
Category : Discontinuous groups
Languages : en
Pages : 200

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Author: Eyal Zvi Goren
Publisher: American Mathematical Soc.
ISBN: 082181995X
Category : Mathematics
Languages : en
Pages : 282

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Book Description
This book is devoted to certain aspects of the theory of $p$-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of $p$-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelianvarieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of $p$-adic Hilbert modular forms and the geometry ofmoduli spaces of abelian varieties are related. This relation is used to study $q$-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-experts. It attempts to provide the necessary background to all concepts exposed in it. It may serve as a textbook for an advanced graduate course.

Author: Friedrich Hirzebruch
Publisher:
ISBN:
Category :
Languages : en
Pages : 100

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Author: Gerard van der Geer
Publisher: Springer Science & Business Media
ISBN: 3642615538
Category : Mathematics
Languages : en
Pages : 301

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Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field.

Author: Hiraku Nakajima
Publisher: American Mathematical Soc.
ISBN: 0821819569
Category : Mathematics
Languages : en
Pages : 146

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Book Description
It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.

Author: Friedrich Hirzebruch
Publisher:
ISBN:
Category : Discontinuous groups
Languages : en
Pages : 108

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Author: T. Oda
Publisher: Springer Science & Business Media
ISBN: 1468492012
Category : Mathematics
Languages : en
Pages : 141

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Author: Jan Hendrik Bruinier
Publisher: Springer Science & Business Media
ISBN: 3540741194
Category : Mathematics
Languages : en
Pages : 273

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Book Description
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Author: Friedrich Hirzebruch
Publisher:
ISBN:
Category : Discontinuous groups
Languages : en
Pages : 103

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Author: T. Oda
Publisher:
ISBN: 9781468492026
Category :
Languages : en
Pages : 144

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Book Description