Hilbert Modular Surfaces

Author : Gerard van der Geer
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642615535

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Hilbert Modular Surfaces by Gerard van der Geer Pdf

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 : Friedrich Hirzebruch,Gerard van der Geer
Publisher : Unknown
Page : 200 pages
File Size : 53,9 Mb
Release : 1981
Category : Discontinuous groups
ISBN : UOM:39015015619466

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Lectures on Hilbert Modular Surfaces by Friedrich Hirzebruch,Gerard van der Geer Pdf

Author : T. Oda
Publisher : Springer Science & Business Media
Page : 141 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492019

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Periods of Hilbert Modular Surfaces by T. Oda Pdf

Author : T. Oda
Publisher : Unknown
Page : 144 pages
File Size : 54,8 Mb
Release : 1982-01-01
Category : Electronic
ISBN : 1468492020

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Periods of Hilbert Modular Surfaces by T. Oda Pdf

Author : Jayce Getz,Mark Goresky
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 49,9 Mb
Release : 2012-03-28
Category : Mathematics
ISBN : 9783034803519

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Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change by Jayce Getz,Mark Goresky Pdf

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

Author : Eyal Zvi Goren,Zvi Goren
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 48,5 Mb
Release : 2002
Category : Abelian varieties
ISBN : 9780821819951

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Lectures on Hilbert Modular Varieties and Modular Forms by Eyal Zvi Goren,Zvi Goren Pdf

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 : Eberhard Freitag
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 52,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662026380

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Hilbert Modular Forms by Eberhard Freitag Pdf

Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a comprehensive presentation of these results, previously scattered in research journal papers, has become obvious. The main aim of this book is to give a description of the singular cohomology and its Hodge decomposition including explicit formulae. The author has succeeded in giving proofs which are both elementary and complete. The book contains an introduction to Hilbert modular forms, reduction theory, the trace formula and Shimizu's formulae, the work of Matsushima and Shimura, analytic continuation of Eisenstein series, the cohomology and its Hodge decomposition. Basic facts about algebraic numbers, integration, alternating differential forms and Hodge theory are included in convenient appendices so that the book can be used by students with a knowledge of complex analysis (one variable) and algebra.

Author : Friedrich Hirzebruch
Publisher : Unknown
Page : 108 pages
File Size : 51,6 Mb
Release : 1973
Category : Discontinuous groups
ISBN : STANFORD:36105031559730

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Hilbert Modular Surfaces by Friedrich Hirzebruch Pdf

Author : Max-Albert Knus,Guido Mislin,Urs Stammbach
Publisher : Unknown
Page : 288 pages
File Size : 54,6 Mb
Release : 1978
Category : Algebra
ISBN : UCAL:B3689453

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Monographie ... de L'enseignement Mathématique by Max-Albert Knus,Guido Mislin,Urs Stammbach Pdf

Author : Gerardus Bartholomeus Maria Van der Geer
Publisher : Unknown
Page : 100 pages
File Size : 49,6 Mb
Release : 1977
Category : Electronic
ISBN : UCAL:B2703478

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On Hilbert Modular Surfaces of Principal Congruence Subgroups by Gerardus Bartholomeus Maria Van der Geer Pdf

Author : Fabrizio Andreatta,Eyal Zvi Goren
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 55,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821836095

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Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects by Fabrizio Andreatta,Eyal Zvi Goren Pdf

We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our methods are geometric - comparing holomorphic Hilbert modular forms with rational functions on a moduli scheme with level-$p$ structure, whose poles are supported on the non-ordinary locus.In the $p$-adic theory we study congruences between Hilbert modular forms. This applies to the study of congruences between special values of zeta functions of totally real fields. It also allows us to define $p$-adic Hilbert modular forms 'a la Serre' as $p$-adic uniform limit of classical modular forms, and compare them with $p$-adic modular forms 'a la Katz' that are regular functions on a certain formal moduli scheme. We show that the two notions agree for cusp forms and for a suitable class of weights containing all the classical ones. We extend the operators $V$ and $\Theta_\chi$ to the $p$-adic setting.

Author : Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 43,9 Mb
Release : 2008-02-10
Category : Mathematics
ISBN : 9783540741190

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The 1-2-3 of Modular Forms by Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier Pdf

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 : Alexander Caspar
Publisher : Unknown
Page : 112 pages
File Size : 47,9 Mb
Release : 2003
Category : Hilbert modular surfaces
ISBN : UOM:39015058213821

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Kummer-Chern-Eisenstein Motives Via Hilbert Modular Surfaces by Alexander Caspar Pdf

Author : Kunihiko Kodaira,W. L. Jr Baily,T. Shioda
Publisher : CUP Archive
Page : 424 pages
File Size : 47,9 Mb
Release : 1977
Category : Mathematics
ISBN : 0521217776

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Complex Analysis and Algebraic Geometry by Kunihiko Kodaira,W. L. Jr Baily,T. Shioda Pdf

The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

Author : Paul B. Garrett
Publisher : Chapman and Hall/CRC
Page : 304 pages
File Size : 46,9 Mb
Release : 1989-09-01
Category : Mathematics
ISBN : 0534103448

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Holomorphic Hilbert Modular Forms by Paul B. Garrett Pdf

An introduction to a substantial part of the theory of holomorphic Hilbert modular forms, associated L-functions, and their arithmetic. As such, it is an introduction to the theory of automorphic forms in general, especially to the arithmetic of holomorphic forms. Annotation copyrighted by Book News, Inc., Portland, OR