Download or read book On the calculation of local terms in the Lefschetz Verdier trace formula and its application to a conjecture of Deligne written by Richard Pink and published by . This book was released on 1991 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Algebraic Geometry to Coding Theory Physics and Computation written by Ciro Ciliberto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.
Download or read book On the Cohomology of Certain Non Compact Shimura Varieties AM 173 written by Sophie Morel and published by Princeton University Press. This book was released on 2010-01-04 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Geometry and Cohomology of Some Simple Shimura Varieties AM 151 written by Michael Harris and published by Princeton University Press. This book was released on 2001-11-04 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.
Download or read book Shimura Varieties written by Thomas Haines and published by Cambridge University Press. This book was released on 2020-02-20 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume forms the sequel to "On the stabilization of the trace formula", published by International Press of Boston, Inc., 2011
Download or read book Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii iv Invited Lectures written by Rajendra Bhatia and published by World Scientific. This book was released on 2011-06-06 with total page 4137 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Download or read book Cohomology of Drinfeld Modular Varieties Part 2 Automorphic Forms Trace Formulas and Langlands Correspondence written by and published by Cambridge University Press. This book was released on with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Cycles and Motives Volume 2 written by Jan Nagel and published by Cambridge University Press. This book was released on 2007-05-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of the subject of algebraic cycles and motives as it stands.
Download or read book Smooth Compactifications of Locally Symmetric Varieties written by Avner Ash and published by Cambridge University Press. This book was released on 2010-01-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry.
Download or read book Endoscopy for GSp 4 and the Cohomology of Siegel Modular Threefolds written by Rainer Weissauer and published by Springer Science & Business Media. This book was released on 2009-03-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of modular curves and the structure of their cohomology groups have been a rich source for various number-theoretical applications over the last decades. Similar applications may be expected from the arithmetic of higher dimensional modular varieties. For Siegel modular threefolds some basic results on their cohomology groups are derived in this book from considering topological trace formulas.
Download or read book Automorphic Representations of Low Rank Groups written by Yuval Zvi Flicker and published by World Scientific. This book was released on 2006 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called ?liftings?. This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E: F] = 2.The book develops the technique of comparison of twisted and stabilized trace formulae and considers the ?Fundamental Lemma? on orbital integrals of spherical functions. Comparison of trace formulae is simplified using ?regular? functions and the ?lifting? is stated and proved by means of character relations.This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent.There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne's (proven) conjecture on the fixed point formula.
Download or read book Groups St Andrews 2009 in Bath Volume 2 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2011-06-16 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Eammon O'Brien, Mark Sapir and Dan Segal, survey the latest developments in algebra.
Download or read book Current Developments in Mathematics written by and published by . This book was released on 1999 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Drinfeld Moduli Schemes and Automorphic Forms written by Yuval Z Flicker and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place. It develops Drinfeld’s theory of elliptic modules, their moduli schemes and covering schemes, the simple trace formula, the fixed point formula, as well as the congruence relations and a "simple" converse theorem, not yet published anywhere. This version, based on a recent course taught by the author at The Ohio State University, is updated with references to research that has extended and developed the original work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as a valuable resource to facilitate an entrance to this fascinating area of mathematics.
Download or read book Mathematical Reviews written by and published by . This book was released on 1999 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automorphic Forms And Shimura Varieties Of Pgsp 2 written by Yuval Z Flicker and published by World Scientific. This book was released on 2005-08-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings.' 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 natural embedding of Sp(2,≤) in SL(4, ≤). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum.Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations.To put these results in a general context, the book concludes with a technical introduction to Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture.
