WorldCat Identities

Shafarevich, I. R. (Igorʹ Rostislavovich) 1923-2017

Works: 285 works in 1,367 publications in 9 languages and 16,237 library holdings
Genres: History  Textbooks 
Roles: Author, Editor, Honoree, Author of introduction, Dedicatee, Other, Contributor
Publication Timeline
Most widely held works by I. R Shafarevich
Number theory by Z. I Borevich( Book )

45 editions published between 1966 and 1995 in English and Undetermined and held by 874 WorldCat member libraries worldwide

Basic algebraic geometry by I. R Shafarevich( Book )

61 editions published between 1972 and 2013 in 4 languages and held by 805 WorldCat member libraries worldwide

Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this do mam. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. Around 1910 Klein wrote: "When I was a student, Abelian functions*-as an after-effect of Jacobi's tradition-were regarded as the undIsputed summit of mathe matics, and each of us, as a matter of course, had the ambition to forge ahead in this field. And now? The young generation hardly know what Abelian functions are." (Vorlesungen tiber die Entwicklung der Mathe matik im XIX. Jahrhundert, Springer-Verlag, Berlin 1926, Seite 312). The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axio matic spirit, which then determined the development of mathematics. Several decades had to lapse before the rise of the theory of topolo gical, differentiable and complex manifolds, the general theory of fields, the theory of ideals in sufficiently general rings, and only then it became possible to construct algebraic geometry on the basis of the principles of set-theoretical mathematics. Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics
Algebra I : basic notions of algebra by I. R Shafarevich( Book )

57 editions published between 1989 and 2014 in 3 languages and held by 802 WorldCat member libraries worldwide

From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 "...which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra.... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers..." The Mathematical Gazette, 1991 "... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions - all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991
Basic algebraic geometry by I. R Shafarevich( Book )

82 editions published between 1994 and 2017 in 5 languages and held by 756 WorldCat member libraries worldwide

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Khler geometry and Hodge theory. The final section raisesan important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics
Geometries and groups by V. V Nikulin( Book )

29 editions published between 1983 and 1994 in English and held by 649 WorldCat member libraries worldwide

This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry."
Algebraic geometry IV : linear algebraic groups, invariant theory by A. N Parshin( Book )

42 editions published between 1988 and 2010 in English and held by 566 WorldCat member libraries worldwide

Dealing with the subject of complex algebraic geometry, this work offers a succinct summary of the areas it covers, while providing coverage of certain important fields. It presents an introduction to the work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties
The socialist phenomenon by I. R Shafarevich( Book )

12 editions published between 1980 and 2013 in English and held by 474 WorldCat member libraries worldwide

Discourses on algebra by I. R Shafarevich( Book )

17 editions published between 2002 and 2009 in English and Japanese and held by 390 WorldCat member libraries worldwide

The classic geometry of Euclid has attracted many for its beauty, elegance, and logical cohesion. In this book, the leading Russian algebraist I.R. Shafarevich argues with examples that algebra is no less beautiful, elegant, and logically cohesive than geometry. It contains an exposition of some rudiments of algebra, number theory, set theory and probability presupposing very limited knowledge of mathematics. I.R. Shafarevich is known to be one of the leading mathematicians of the 20th century, as well as one of the best mathematical writers
Arithmetic and geometry : papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday by I. R Shafarevich( Book )

31 editions published in 1983 in English and held by 357 WorldCat member libraries worldwide

Algebraic geometry I : algebraic curves, algebraic manifolds and schemes by V. I Danilov( Book )

23 editions published between 1988 and 2007 in English and held by 357 WorldCat member libraries worldwide

The algebraic material also treats algebraic curves over an arbitrary field and the connection between algebraic curves and Abelian varieties. The second part is an introduction to higher-dimensional algebraic geometry. The author deals with algebraic varieties, the corresponding morphisms, the theory of coherent sheaves and, finally, the theory of schemes
Number theory II : algebraic number theory by Helmut Koch( Book )

20 editions published in 1992 in English and Italian and held by 323 WorldCat member libraries worldwide

From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: " ... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 " ... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
Algebra II : noncommutative rings, identities by A. I Kostrikin( Book )

12 editions published in 1991 in English and Undetermined and held by 316 WorldCat member libraries worldwide

The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra - Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le
Number theory I : fundamental problems, ideas and theories by I︠U︡. I Manin( Book )

21 editions published between 1992 and 1995 in English and held by 288 WorldCat member libraries worldwide

This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry
Algebra VII : combinatorial group theory, applications to geometry by A. N Parshin( Book )

15 editions published between 1991 and 1993 in 3 languages and held by 285 WorldCat member libraries worldwide

From the reviews of the first printing of this book, published as volume 58 of the Encyclopaedia of Mathematical Sciences: " ... This book will be very useful as a reference and guide to researchers and graduate students in algebra and and topology." Acta Scientiarum Mathematicarum, Ungarn, 1994 " ... The book under review consists of two monographs on geometric aspects of group theory: Combinatorial group theory and fundamental groups" by D.J. Collins and H. Zieschang ... : "Some problems of group theory related to geometry" by R.I. Grigorchuk and P.F. Kurchanov. ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ... In summary, a very interesting book! Bulletin of the London Mathematical Society, 1996 " ... In both essays the authors give clear and comprehensive definitions, examples and statements (but not proofs) of theorems, so that the book can be understood by a reader with a minimal background in group theory or geometry. Such a reader, needing to find out what is known in this area, will find this a full and accessible store of information." Contemporary Physics, 1994 " ... This survey (Part II) presents for the first time that problems in monograph form and by the way offers a unifying treatment of the various approaches to their solutions, as far as they are known, together with hints to open problems. A titbit for every interested reader!" Monatshefte für Mathematik, 1995
Algebra V : homological algebra by A. I Kostrikin( Book )

15 editions published between 1990 and 1994 in English and held by 277 WorldCat member libraries worldwide

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology
Algebraic geometry II : cohomology of algebraic varieties, algebraic surfaces( Book )

19 editions published between 1996 and 2014 in English and held by 268 WorldCat member libraries worldwide

"This EMS volume consists of two parts. The first part is devoted to cohomology of algebraic varieties. The second part deals with algebraic surfaces. The authors, who are well-known experts in the field, have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics."--BOOK JACKET. "This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetical algebraic geometry, complex analysis and related fields."--BOOK JACKET
Algebraic surfaces by I. R Shafarevich( Book )

21 editions published between 1965 and 1997 in 3 languages and held by 267 WorldCat member libraries worldwide

Number theory IV : transcendental numbers by I. R Shafarevich( Book )

20 editions published between 1992 and 2011 in English and Italian and held by 257 WorldCat member libraries worldwide

This book is a survey of the most important directions of research in transcendental number theory. The central topics in this theory include proofs of irrationality and transcendence of various numbers, especially those that arise as the values of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle, which Lindemann showed to be impossible in 1882, when he proved that $Öpi$ is a transcendental number. Euler's conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert's famous list of open problems; this conjecture was proved by Gel'fond and Schneider in 1934. A more recent result was ApÖ'ery's surprising proof of the irrationality of $Özeta(3)$ in 1979. The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different branches of number theory, this monograph provides both an overview of the central ideas and techniques of transcendental number theory, and also a guide to the most important results
Linear algebra and geometry by I. R Shafarevich( Book )

17 editions published between 2012 and 2014 in English and held by 124 WorldCat member libraries worldwide

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics
Number theory, algebra, and algebraic geometry by A. I Kostrikin( Book )

15 editions published between 1995 and 2004 in English and held by 88 WorldCat member libraries worldwide

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Geometries and groups
Alternative Names
Chafarevich, I. R.

Chafarevich, Igor Rostislavovich

Chafarevitch, I. 1923-

Chafarevitch, I. R.

Chafarevitch, I. R. 1923-

Chafarevitch, I. R., 1923-2017

Chafarévitch, Igor

Chafarévitch, Igor 1923-

Chafarévitch, Igor 1923-2017

Chafarevitch, Igor R.

Chafarevitch, Igor R. 1923-

Chafarevitch, Igor R. 1923-2017

Chafarevitch, Igor R. (Igor Rostislavovich), 1923-

Chafarevitch, Igor Rostislavovitch.

Chafarevitch Igor Rostislavovitch 1923-....

Chafarevitch, Igor Rostislavovitch 1923-2017

Igor Chafarevitch mathématicien russe

Igor' Rostislavovič Šafarevič matematico sovietico

Igor Rostislawowitsch Schafarewitsch russischer Mathematiker

Igor Ŝafareviĉ Rusa matematikisto

Igor Șafarevici

Igor Safarevics orosz matematikus

Igor Šafarevitš

Igor Šafarevõtš

Igor Shafarevich matemático ruso

Igor Shafarevich Russian mathematician

Igor Shafarevich Soviet and Russian mathematician

Igor Sjafarevitsj Russisch wiskundige

Igor Sjafarevitsj russisk matematikar

Igor Sjafarevitsj russisk matematiker

Igor Szafariewicz

Šafarevič, I. 1923-

Šafarevič, I. 1923-2017

Šafarevič, I. R.

Šafarevič, I. R. 1923-

Šafarevič, I.R. 1923-2017

Šafarevič, Igorʹ.

Šafarevič, Igor' 1923-

Šafarevič, Igor' 1923-2017

Safarevic, Igor R.

Šafarevič, Igor R. 1923-

Šafarevič, Igor R., 1923-2017

Šafarevič, Igorʹ Rostislavovič

Šafarevič, Igorʹ Rostislavovič 1923-

Šafarevič, Igorʹ Rostislavovič 1923-2017

Șafarevici, I. R. 1923-

Șafarevici, I. R., 1923-2017

Safarevié, Igor 1923-

Schafarewitsch, I.R.

Schafarewitsch, I. R. 1923-

Schafarewitsch, I. R. 1923-2017

Schafarewitsch, Igor.

Schafarewitsch, Igor R.

Schafarewitsch Igor R. 1923-....

Schafarewitsch, Igor R. 1923-2017

Schafarewitsch, Igor Rostislavovitsch 1923-

Shafarevich, I.R.

Shafarevich, I.R. 1923-

Shafarevich, I. R. 1923-2017

Shafarevich, I. R. (Igor Rostislavovich)

Shafarevich, I. R. (Igorʹ Rostislavovich), 1923-

Shafarevich, Igor

Shafarevich, Igor 1923-

Shafarevich, Igor R.

Shafarevich Igor R. 1923-....

Shafarevich, Igor' R. 1923-2017

Shafarevich, Igor' Rostislavich

Shafarevich, Igorʹ Rostislavovich

Shafarevich, Igorʹ Rostislavovich 1923-

Shafarevich, Igorʹ Rostislavovich, 1923-2017

Sjafarevitsj, I.R. 1923-

Sjafarewitsj, I.R. 1923-

Szafariewicz, Igor.

Szafariewicz, Igor 1923-

Szafariewicz, Igor, 1923-2017

Xafarevitx, Igor R. 1923-

Игор Шафаревич

Шафаревич, И. Р 1923-

Шафаревич, И. Р. (Игорь Ростиславович), 1923-2017

Шафаревич, Игор Ростилавович 1923-...

Шафаревич, Игор Ростилавович, 1923-2017

Шафаревич, Игор Ростиславович.

Шафаревич, Игорь 1923-

Шафаревич, Игорь (Игорь Ростиславович), 1923-

Шафаревич, Игорь Ростиславович.

Шафаревич, Игорь Ростиславович 1923-...)

Шафаревич, Игорь Ростиславович, 1923-2017

Шафаревич Ігор Ростиславович

Ігар Расціслававіч Шафарэвіч

ایقور شافرویچ

이고리 샤파레비치



シャファレヴィッチ, イゴール R


Basic algebraic geometryAlgebra I : basic notions of algebraBasic algebraic geometryGeometries and groupsAlgebraic geometry IV : linear algebraic groups, invariant theoryDiscourses on algebraAlgebraic geometry I : algebraic curves, algebraic manifolds and schemesAlgebra VII : combinatorial group theory, applications to geometry