Download or read book Hilbert Modular Surfaces written by Gerard van der Geer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Periods of Hilbert Modular Surfaces written by T. Oda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Hilbert Modular Surfaces written by Friedrich Hirzebruch and published by . This book was released on 1981 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hilbert Modular Surfaces written by Friedrich Hirzebruch and published by . This book was released on 1973 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Periods of Hilbert Modular Surfaces written by T. Oda and published by . This book was released on 1982-01-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Hilbert Modular Surfaces Which Are of the General Type written by Tsz-On Mario Chan and published by Open Dissertation Press. This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Hilbert Modular Surfaces Which Are of the General Type" by Tsz-on, Mario, Chan, 陳子安, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled ON HILBERT MODULAR SURFACES WHICH ARE OF THE GENERAL TYPE submitted by Chan Tsz On Mario for the degree of Master of Philosophy at The University of Hong Kong in November 2007 Compact Riemann surfaces are classified according to their genera. For a surface of genus>= 2, the uniformization theorem says that it is a quotient Γ\∆ of the unit disc ∆ by a discrete subgroup Γ of Aut(∆), acting freely on ∆. In general, the quotient Γ\∆ for an arbitrary dis- crete subgroup Γ∈ Aut(∆) is considered. It is equivalent to consider X = Γ\H, where H is the upper half plane and Γ a discrete subgroup ofAut(H) =PSL (R). Thisspacecanbegivenastructureofmanifold, but may not be compact in general. When Γ is a subgroup commensu- rable withPSL (Z), X is called a modular curve. There is a procedure to compactify X by adding finite number of points, and the resultinge spaceX canbegiventhestructureofacompactRiemannsurface. The properties of X can be studied according to the genus of X. In the theory of compact complex surfaces, there is a rough clas- sification according to the Kodaira dimensions. A surface of Kodaira dimension 2 is called a surface of general type and is analogous to the Riemann surfaces of genus>= 2. Parallel to modular curves, one would study the quotient of HH by a discrete group commensurable with a Hilbert modular groupPSL (o ), where o is the ring of integers of 2 K K a real quadratic field K overQ. These spaces are called Hilbert modu- lar surfaces. PSL (o ) is irreducible, i.e. whenPSL (K) is embedded 2 K 2 into PSL (R)PSL (R), the image of PSL (o ) under each projec- 2 2 2 K tion is dense in PSL (R). Therefore the Hilbert modular surfaces are not simply products of modular curves. There is also a procedure to compactify such quotients by adding finite number of points. Contrary to the case of modular curves, the compact spaces thus obtained are highly singular. Hirzebruch gave a procedure to desingularize them. As a result, Hilbert modular surfaces can be studied using theory of compact complex surfaces. Hilbert modular surfaces have a deep rootin number theory. Because of this nature, one can calculate explic- itly the geometric invariants of them in terms of algebraic parameters. Their types according to the rough classification can then be found. This thesis aims at demonstrating how a Hilbert modular surface can be identified to be of general type. To provide necessary back- ground of the one-dimensional theory, it presents the basic theories of compactRiemannsurfacesandmodularcurvesindetail, andillustrates how the theory of compact Riemann surfaces can be applied to study modular curves. Hilbert modular surfaces were then introduced as an analogue of modular curves. Hirzebruch's procedure of desingulariza- tion was described. Analogous to the one-dimensional cases, the application of the the- ory of compact complex surfaces to Hilbert modular surfaces was illus- trated by demonstrating how the geometric invariants of the surfaces canbecalculatedfromthealgebraicparameters. Attheendofthethe- sis, a sufficient condition for a Hilbert modular surface to be of general type was given. DOI: 10.5353/th_b3955766 Subjects: Hilbert modular surfaces
Download or read book Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change written by Jayce Getz and published by Springer Science & Business Media. This book was released on 2012-03-28 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modular Embeddings of Hilbert Modular Surfaces written by Eberhard Freitag and published by . This book was released on 2003 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hilbert Modular Forms written by Eberhard Freitag and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Hilbert Modular Surfaces of Principal Congruence Subgroups written by Gerardus Bartholomeus Maria Van der Geer and published by . This book was released on 1977 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cusps of Hilbert Modular Surfaces and 4 folds written by Stephen Meagher and published by . This book was released on 2004 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Hilbert Modular Surfaces which are of the General Type written by Tsz-on Chan (Mario) and published by . This book was released on 2007 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Hilbert Modular Varieties and Modular Forms written by Eyal Zvi Goren and published by American Mathematical Soc.. This book was released on 2002 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hilbert Modular Surfaces written by and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hilbert Modular Surfaces with P G leq 1 written by Y. Hamahata and published by . This book was released on 1993 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hilbert Modular Surfaces written by Friedrich Hirzebruch and published by . This book was released on 1973 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hilbert Modular Surfaces written by Friedrich Hirzebruch and published by . This book was released on 1973 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt:
