Arithmetical Compactification Of Mixed Shimura Varieties
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Author | : Richard Pink |
Publisher | : |
Total Pages | : 368 |
Release | : 1989 |
Genre | : Algebraic varieties |
ISBN | : |
Download Arithmetical Compactification of Mixed Shimura Varieties Book in PDF, Epub and Kindle
Author | : Fritz Hörmann |
Publisher | : |
Total Pages | : 152 |
Release | : 2014 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 9781470419585 |
Download The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type Book in PDF, Epub and Kindle
Cover -- Title page -- Contents -- Overview -- Integral models of toroidal compactifications of mixed Shimura varieties -- Volumes of orthogonal Shimura varieties -- Appendix A -- Appendix B -- Bibliography -- Index -- Table of notation -- Back Cover
Author | : Fritz Hörmann |
Publisher | : American Mathematical Society |
Total Pages | : 162 |
Release | : 2014-11-05 |
Genre | : Mathematics |
ISBN | : 1470419122 |
Download The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type Book in PDF, Epub and Kindle
This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula--an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special derivatives of such Eisenstein series. This result gives substantial evidence in the direction of Kudla's conjectures in arbitrary dimensions. The validity of the full set of conjectures of Kudla, in turn, would give a conceptual proof and far-reaching generalizations of the work of Gross and Zagier on the Birch and Swinnerton-Dyer conjecture. Titles in this series are co-published with the Centre de Recherches Mathématiques.
Author | : |
Publisher | : World Scientific |
Total Pages | : 1191 |
Release | : |
Genre | : |
ISBN | : |
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Author | : Thomas Haines |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2020-02-20 |
Genre | : Mathematics |
ISBN | : 1108704867 |
Download Shimura Varieties Book in PDF, Epub and Kindle
This volume forms the sequel to "On the stabilization of the trace formula", published by International Press of Boston, Inc., 2011
Author | : Richard Pink |
Publisher | : |
Total Pages | : |
Release | : 1990 |
Genre | : |
ISBN | : |
Download Arithmetical Compactification of Mixed Shimura Varieties Book in PDF, Epub and Kindle
Author | : A. J. Scholl |
Publisher | : Cambridge University Press |
Total Pages | : 506 |
Release | : 1998-11-26 |
Genre | : Mathematics |
ISBN | : 0521644194 |
Download Galois Representations in Arithmetic Algebraic Geometry Book in PDF, Epub and Kindle
Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.
Author | : Kai-Wen Lan |
Publisher | : |
Total Pages | : 2154 |
Release | : 2008 |
Genre | : |
ISBN | : |
Download Arithmetic Compactifications of PEL-type Shimura Varieties Book in PDF, Epub and Kindle
In this thesis, we constructed minimal (Satake-Baily-Borel) compactifications and smooth toroidal compactifications of integral models of general PEL-type Shimura varieties (defined as in Kottwitz [79]), with descriptions of stratifications and local structures on them extending the well-known ones in the complex analytic theory. This carries out a program initiated by Chai, Faltings, and some other people more than twenty years ago. The approach we have taken is to redo the Faltings-Chai theory [37] in full generality, with as many details as possible, but without any substantial case-by-case study. The essential new ingredient in our approach is the emphasis on level structures, leading to a crucial Weil pairing calculation that enables us to avoid unwanted boundary components in naive constructions.
Author | : Min Ho Lee |
Publisher | : Springer Science & Business Media |
Total Pages | : 262 |
Release | : 2004-05-13 |
Genre | : Computers |
ISBN | : 9783540219224 |
Download Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms Book in PDF, Epub and Kindle
This volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a comprehensive exposition of mixed automorphic forms that has never yet appeared in book form. The main goal is to explore connections among complex torus bundles, mixed automorphic forms, and Jacobi forms associated to an equivariant holomorphic map. Both number-theoretic and algebro-geometric aspects of such connections and related topics are discussed.
Author | : Sophie Morel |
Publisher | : Princeton University Press |
Total Pages | : 230 |
Release | : 2010-01-31 |
Genre | : Mathematics |
ISBN | : 0691142920 |
Download On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) Book in PDF, Epub and Kindle
This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of finite adelic points of G. The second action can be studied on the set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois action--at good places--on the G(Af)-isotypical components of the cohomology. Morel uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula. The first problem, that of applying the fixed point formula to the intersection cohomology, is geometric in nature and is the object of the first chapter, which builds on Morel's previous work. She then turns to the group-theoretical problem of comparing these results with the trace formula, when G is a unitary group over Q. Applications are then given. In particular, the Galois representation on a G(Af)-isotypical component of the cohomology is identified at almost all places, modulo a non-explicit multiplicity. Morel also gives some results on base change from unitary groups to general linear groups.