Author: S.-V. Stratila
Publisher: Springer
ISBN: 3540379169
Category : Mathematics
Languages : en
Pages : 178

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Book Description

Author: S. V. Stratila
Publisher:
ISBN: 9783662206683
Category :
Languages : en
Pages : 188

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Book Description

Author: Peter Gabriel
Publisher: Springer Science & Business Media
ISBN: 9783540629900
Category : Mathematics
Languages : en
Pages : 188

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Book Description
From the reviews: "... [Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature. ..." --The Mathematical Gazette

Author: J. S. Milne
Publisher: Cambridge University Press
ISBN: 1107167485
Category : Mathematics
Languages : en
Pages : 665

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Book Description
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Author: Yuval Zvi Flicker
Publisher: World Scientific
ISBN: 9812568034
Category : Political Science
Languages : en
Pages : 499

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Book Description
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.

Author: George M. Bergman
Publisher: Springer
ISBN: 3319114786
Category : Mathematics
Languages : en
Pages : 574

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Book Description
Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Author: William Fulton
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 120

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Book Description
The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals and polynomials, such as is often covered in a one-semester course in modern algebra; additional commutative algebra is developed in later sections.

Author: Michael F. Atiyah
Publisher: CRC Press
ISBN: 0429973268
Category : Mathematics
Languages : en
Pages : 140

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Book Description
First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

Author: Igor V. Nikolaev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110788810
Category : Mathematics
Languages : en
Pages : 292

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Book Description
Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.

Author: Andreas Kriegl
Publisher: American Mathematical Society
ISBN: 1470478935
Category : Mathematics
Languages : en
Pages : 631

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Book Description
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.