Hilbert Modular FormsMod P And P-adic Aspects (Memoirs of the American Mathematical Society)
- 100 Pages
- February 2005
- 2.36 MB
- 8046 Downloads
American Mathematical Society
Algebraic geometry, Algebraic number theory, Geometry - Algebraic, Mathematics, Arithmetical algebraic geometr, Arithmetical algebraic geometry, Forms, Modular, Hilbert modular surfaces, Moduli t
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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 : Springer-Verlag Berlin Heidelberg. The theory of $p$-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N.
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 by: 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.
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 by: The present notes contain the material of the lectures given by the author at the summer school on “Modular Forms and their Applications” at the Sophus Lie Conference Center in the summer of We give an introduction to the theory of Hilbert modular forms and some geometric and arithmetic by: Hilbert modular forms and their applications 3 I thank G.
van der Geer and D. Zagier for several interesting conversations during the summer school at the Sophus Lie Conference Center. Moreover, I thank J. Funke for his helpful comments on a ﬁrst draft of this manuscript.
1 Hilbert modular surfaces. Hilbert modular forms and varieties Applications of Hilbert modular forms The Hilbert Modular Forms book conjecture for Hilbert modular forms The next three lectures: goal Notations F is a totally real number ﬁeld of degree g.
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JF is the set of all real embeddings of F. For each τ ∈ JF, we denote the corresponding embedding into R by a 7→aτ.
I know of two pretty good books on Hilbert modular forms: Garrett's "Holomorphic Hilbert Modular Forms" and Freitag's Hilbert Modular forms.
The latter only covers classical Hilbert modular forms whereas the former introduces both classical and adelic Hilbert modular forms. Elliptic Modular Forms and Their Applications 3 1 Basic Deﬁnitions In this section we introduce the basic objects of study – the group SL(2,R) and its action on the upper half plane, the modular group, and holomorphic modular forms – and show that the space of modular forms of any weight and level is Size: 1MB.
Representations of Galois groups associated to Hilbert modular forms, Richard Taylor. The Lefschetz trace formula for an open algebraic surface, Thomas Zink. L 2 -cohomology of Shimura varieties, Steven Zucker. This book, authored by a leading researcher, describes the striking applications that have been found for this technique.
Hilbert Modular Forms and Iwasawa Theory - Haruzo Hida - Oxford University Press. 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. 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. Katz and J.-P. Serre. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms.
Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W.
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. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.
2, Hilbert and Siegel modular forms, trace formulas, p-adic modular forms, and modular abelian varieties, all of which are topics for additional books.
We also rarely analyze the complexity of the algorithms, but instead settle for occasional remarks about their practical eﬃciency.
For most of this book we assume the reader has some prior File Size: 2MB. Errata and Addenda as of December 1, Hilbert Modular Forms and Iwasawa Theory Oxford University Press, Here is a table of misprints in the above book, and “P.3 L.5b” indicates ﬁfth line from the bottom of the.
systematically the geometric and arithmetic aspects of Hilbert modular varieties and to apply them to modular forms.
As to be expected in such a project, we Mathematics Subject Classi cation. Primary 11G18, 14G35, 11F33, 11F Key words: Congruence, Hilbert modular form, Hilbert modular variety, zeta function, l-tration. Hida, p-Adic Automorphic Forms on Shimura Varieties, Springer Monographs in Mathematics,[Springer link], [Springer web site on this book], A list of misprints (as of 6/26/07): H.
Hida, Hilbert Modular Forms and Iwasawa Theory, Oxford Mathematical Monographs, Oxford University Press, [Oxford web site on this book]. This chapter focuses on multi-tensors of differential forms on the Hilbert modular variety and on its subvarieties. It presents an assumption where Γ K a Hilbert modular group associated with a totally real algebraic number field K of degree n > 1.
T K is considered as a Hilbert modular variety H n /Γ K. Hilbert modular forms Hilbert modular forms. We quickly recall some of the basic theory of Hilbert modular forms attached to quadratic elds. The book  introduces Hilbert modular forms with a view toward Borcherds products and is therefore a useful reference for more details.
Let H be the usual upper half. Hilbert modular forms are functions in n variables, each a complex number in the upper half-plane, satisfying a modular relation for 2×2 matrices with entries in a totally real number field. $\begingroup$ Note that Theorem of Miyake's book on modular forms is a reference for the statement over the rationals.
I wonder whether vytas' answer can somehow be translated into a similar "low-level" proof of the assertion in the Hilbert case. $\endgroup$ – Kevin Buzzard Oct 22 '10 at |. An example of a non-paritious Hilbert modular form.
Kevin Buzzard Ap 1 Background and de nitions. [written Dec ] A good source for notation and de nitions is the paper . We start by summarising some of this paper.
Details Hilbert Modular Forms FB2
Let F be a totally real eld of degree nover Q, with integers O. Note: Shimura uses some other funny letter, not O. 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. Some of the standard books on Hilbert modular forms like Freitag , Garrett  or van der Geer  do not have what we want; although Garrett’s book Date: J on with the best of my energies in the last year and a half have been the book “Lecture Notes on Hilbert Modular Varieties and Modular Forms”, assisting Prof.
Eyal Z. Goren, and this thesis. Accepting to study and work with Prof. Goren has clearly been the single most labor-inducing decision in my mathematical life.
In spite of his occasional. What is a modular form. 5 Course plan 5 Chapter 1. Introduction 7 Math Problem set 1 (due 15/9/09) 8 Hilbert modular forms 60 Siegel modular forms 60 Bibliography 61 Bibliography 61 4.
The chapter on Fuchsian groups is based on the book of Katok. Other references include: Iwaniec Iwaniec 5 Iwaniec-Kowalski Shimura73 6 File Size: KB. This book describes a generalization of their techniques to Hilbert modular forms (towards the proof of the celebrated ‘R=T’ theorem) and applications of the theorem that have been found.
Applications include a proof of the torsion of the adjoint Selmer group (over a totally real field F and over the Iwasawa tower of F) and an explicit formula of the L-invariant of the arithmetic p Author: Haruzo Hida. as divisors of certain meromorphic Hilbert modular forms.
Description Hilbert Modular Forms FB2
More precisely, Borcherds constructed a lift from certain weakly holomorphic modular forms in to Hilbert modular forms with the help of a theta lift. The resulting Hilbert modular form has a inﬁnite product expansion and its divisor is given by a linear.Modular cycles 46 Integration 48 Chapter 5.
Generalities on Hilbert Modular Forms and Varieties 51 Hilbert modular Shimura varieties 52 Hecke congruence groups 53 Weights 54 Hilbert modular forms 55 Cohomological normalization 58 Hecke operators 59 The Petersson inner product 61 Newforms 64 ON OVERCONVERGENT HILBERT MODULAR CUSP FORMS par Fabrizio Andreatta, Adrian Iovita & Vincent Pilloni R esum e.
| We p-adically interpolate modular invertible sheaves over a strict neighborhood of the ordinary locus of an Hilbert modular variety. We then prove the existence of nite slope families of cuspidal eigenforms.
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