# Automorphic Forms and Shimura Varieties of PGSp(2)

by Yuval Z. Flicker

Publisher: World Scientific Publishing Company

Written in English

## Subjects:

• Number Theory,
• Science/Mathematics,
• Mathematics,
• Algebra - General,
• Automorphic forms,
• Shimura varieties,
• Symplectic groups
The Physical Object
FormatHardcover
Number of Pages324
ID Numbers
Open LibraryOL9197295M
ISBN 109812564039
ISBN 109789812564030

We use cookies to make interactions with our website easy and meaningful, to better understand the use of our services, and to tailor advertising. Abstract. We generalize the Shimura–Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group $\mathrm {Mp}_2$, to the metaplectic group $\mathrm {Mp}_{2n}$ of higher rank.   Automorphic forms, Shimura varieties, and L-functions. Vol. I. Proceedings of the conference held at the University of Michigan, Ann Arbor, Michigan, July 6–16, Edited by Laurent publication of Shimura’s book, Shimura (b), and that was the start of an explosion. Automorphic forms and shimura varieties of PGSp(2), Yuval Flicker, World Scientific, Frontiers in Number Theory, Physics, and Geometry I, P. Cartier, B. Julia, P. Moussa, P. Vanhove, (Eds.) Springer History of the Theory of Numbers Leonard Eugene Dickson, Dover reprint,

The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a . Introduction to Shimura varieties and automorphic vector bundles Niccol o Ronchetti February 1 Motivation Let’s recall rst the classical story. One considers the upper half plane H and wants to study modular functions, or modular forms f: H ÝÑC - these are holomorphic functions which have. Automorphic forms and Shimura varieties of PGSp(2) / by Yuval Z. Flicker. PUBLISHER: Singapore: World Scientific, c CALL NUMBER: QA A9 F55 CIMM Sausalito, Calif.: University Science Books, c CALL NUMBER: QC W32 CIMM: TITLE: Search methodologies: introductory tutorials in optimization and decision support. Click Get Books and find your favorite books in the online library. Create free account to access unlimited books, fast download and ads free! We cannot guarantee that Character Identities In The Twisted Endoscopy Of Real Reductive Groups book is in the library. READ as many books .

The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations Some problems in .

## Automorphic Forms and Shimura Varieties of PGSp(2) by Yuval Z. Flicker Download PDF EPUB FB2

Automorphic forms and Shimura varieties of PGSp (2) Yuval Z Flicker This book furthers new and exciting developments in experimental designs, multivariate analysis, biostatistics, model selection and.

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This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1.

An elementary construction of Shimura varieties as moduli of abelian schemes. p-adic deformation theory of automorphic forms on Shimura varieties. Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc. Automorphic Forms and Shimura Varieties of PGSp(2), pp.

() No Access. Automorphic Forms and Shimura Varieties of PGSp(2) Metrics. Downloaded 12 times History. Keywords. Automorphic Representations. This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1.

An elementary construction of Shimura varieties as moduli of abelian schemes. p-adic deformation theory of automorphic forms on Shimura varieties.

A simple proof of irreducibility of the generalized Igusa. The book will certainly be useful to graduate students and researchers entering this beautiful and difficult area of research." (Andrzej Dabrowski, Zentralblatt MATH, Vol.) "The purpose of this book is twofold: First to establish a p-adic deformation theory of automorphic forms on Shimura varieties; this is recent work of the author.

Download Automorphic Forms And Shimura Varieties Of Pgsp 2 books, The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms.

A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois. Shimura Varieties Ordinary p-Adic Automorphic Automorphic Forms and Shimura Varieties of PGSp book Includes bibliographical references (pages ) and indexes Introduction -- Geometric reciprocity laws -- Modular curves -- Hilbert modular varieties -- Generalized Eichler-Shimura map -- Moduli schemes -- Shimura varieties -- Ordinary p-adic automorphic forms.

This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1.

An elementary construction of Shimura varieties as moduli of abelian schemes 2. p-adic deformation theory of automorphic forms on Shimura varieties 3. This book is a high-level exposition of the theory for automorphic forms on Shimura Varieties. It includes a discussion of the special cases of elliptic modular forms and Hilbert modular forms, so it will be a useful resource for those wanting to learn the subject.

The exposition is very dense, however, and the prerequisites are : $5. Coherent cohomology and automorphic forms 52 References 54 Introduction The cohomology of Shimura varieties are of interest and importance in the Lang-lands program as there Galois representations and Hecke modules meet each other (for the ﬁrst time). Let pG,Xq be a Shimura datum, ShpG,XqK be the associ. Get this from a library. Automorphic forms and Shimura varieties of PGSp (2). [Yuval Z Flicker] -- The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating. Type: BOOK - Published: - Publisher: Cambridge University Press Get Books Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. Automorphic forms and representations Decomposition of representations into tensor products By D. FLATH Classical and adelic automorphic forms. An introduction By I. PIATETSKI-SHAPIRO Automorphic forms and automorphic representations By A. BOREL and H. JACQUET On the notion of an automorphic representation. A supplement to the. Automorphic Forms, Shimura Varieties, and L-functions: Proceedings of a Conference Held at the University of Michigan, Ann Arbor, July, Volume 2 Laurent Clozel, J. Milne Academic Press, - Mathematics - pages. The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on. "This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: an elementary construction of Shimura varieties as moduli of abelian schemes; p-adic deformation theory of automorphic forms on Shimura varieties; and a simple proof of irreducibility of the generalized. Automorphic Forms and Shimura Varieties of PGSp(2) This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the. Download E-books p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics) PDF. By Haruzo Hida. This e-book proposes new notions of coherent geometric constitution to supply a clean method of this general box. It develops a brand new idea of self-similarity referred to as "BPI" or "big items of itself," which makes. Buy Automorphic Forms, Shimura Varieties and L-functions, Vol. 1: Proceedings of a Conference Held at the Unviversity of Michigan, Ann Arbor, July(Perspectives in Mathematics, Vol. 10) on FREE SHIPPING on qualified ordersFormat: Hardcover. After preliminaries--including a section, Notation and Terminology''--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity-law for the values of automorphic functions at CM-points is proved. James Arthur, Automorphic representations of${\rm GSp(4)}$, Contributions to automorphic forms, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore, MD,pp. 65– MR [AC] James Arthur and Laurent Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies. Automorphic forms realized in the cohomology of a Shimura variety are more amenable to study than general automorphic forms; in particular, there is a construction attaching. Books: Here's a link to a text reviewed by the MAA: Introduction to the Arithmetic Theory of Automorphic Functions by Goro Shimura. At amazon, you can Look Inside. Also @amazon: Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics), by Daniel Bump. Video Lectures. Automorphic Forms and Shimura Varieties of PGSp (2) () Matching of Orbital Integrals on GL (4) and GSp (2) (). Automorphic Forms And Galois Representations. Download and Read online Automorphic Forms And Galois Representations ebooks in PDF, epub, Tuebl Mobi, Kindle Book. Get Free Automorphic Forms And Galois Representations Textbook and unlimited access to our library by created an account. Fast Download speed and ads Free. Here is a 85MB scan of Shimura's book. You should buy this book at for about 30 bucks.$ and the congruence subgroups of it.

Chapter 2, "Automorphic forms and functions", contains the foundations of the theory of automorphic forms and functions for Fuchsian groups of the first kind, including the evaluation of the. Automorphic forms and Shimura varieties of PGSp(2); +xi pages; World Scientific, AugustISBN Part 1.

Lifting automorphic forms of PGp(2) and SO(4) to PGL(4). Part 2. Zeta functions of Shimura varities of PGSp(2). Part 3. Background on automorphic forms.

Automorphic forms on PGSp(2); notes based on a talk at ArbeitstagungMPI f\"ur Mathematik, Bonn preprint series, On the symmetric square: Automorphic representations of low rank groups ; pp; book in 3 parts: Part 1.

This book, which developed from a course taught in France, is a high-level exposition of the theory for automorphic forms on Shimura Varieties.

It includes a discussion of the special cases of elliptic modular forms and Hilbert modular forms, so it will be a useful resource for. The Hodge-Tate period map is an important, new tool for studying the geometry of Shimura varieties, p-adic automorphic forms and torsion classes in the cohomology of Shimura varieties.

It is a G(A_f)-equivariant map from a perfectoid Shimura variety into a flag variety with only an action of G(Q_p) and can be thought of as a p-adic analogue of.The Gross-Zagier Formula on Shimura Curves: (AMS) - Ebook written by Xinyi Yuan, Shou-wu Zhang, Wei Zhang.