WorldCat Identities

Serre, Jean-Pierre 1926-

Works: 350 works in 1,625 publications in 10 languages and 18,669 library holdings
Genres: Conference papers and proceedings  Personal correspondence  Sources  History 
Roles: Author, Editor, Collector, Other, Author of introduction, Interviewee, Opponent, 956, htt, Commentator, Creator
Classifications: QA171, 512.2
Publication Timeline
Most widely held works about Jean-Pierre Serre
Most widely held works by Jean-Pierre Serre
Linear representations of finite groups by Jean-Pierre Serre( Book )

93 editions published between 1966 and 2014 in 6 languages and held by 1,467 WorldCat member libraries worldwide

This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental result of constant use in mathematics as well as in quantum chemistry or physics. The examples in this part are chosen from those useful to chemists. The second part is a course given in 1966 to second-year students of l'Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory. Several Applications to the Artin representation are given
A course in arithmetic by Jean-Pierre Serre( Book )

72 editions published between 1970 and 2013 in 5 languages and held by 1,244 WorldCat member libraries worldwide

This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor­ phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors
Algèbres de Lie semi-simples complexes by Jean-Pierre Serre( Book )

54 editions published between 1966 and 2017 in 3 languages and held by 1,121 WorldCat member libraries worldwide

These short notes, already well-known in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers, including classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and linear representations. The last chapter discusses the connection between Lie algebras, complex groups and compact groups; it is intended to guide the reader towards further study
Local fields by Jean-Pierre Serre( Book )

65 editions published between 1962 and 2013 in 4 languages and held by 1,119 WorldCat member libraries worldwide

The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray
Lie algebras and Lie groups; 1964 lectures given at Harvard University by Jean-Pierre Serre( Book )

51 editions published between 1965 and 2006 in 3 languages and held by 1,101 WorldCat member libraries worldwide

This book reproduces J-P. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large
Galois cohomology by Jean-Pierre Serre( Book )

69 editions published between 1963 and 2013 in 4 languages and held by 897 WorldCat member libraries worldwide

Algèbre locale, multiplicités; cours au Collège de France, 1957-1958 by Jean-Pierre Serre( Book )

70 editions published between 1965 and 2002 in 5 languages and held by 799 WorldCat member libraries worldwide

This edition reproduces the 2nd corrected printing of the 3rd edition of the now classic notes by Professor Serre, long established as one of the standard introductory texts on local algebra. Referring for background notions to Bourbaki's "Commutative Algebra" (English edition Springer-Verlag 1988), the book focusses on the various dimension theories and theorems on mulitplicities of intersections with the Cartan-Eilenberg functor Tor as the central concept. The main results are the decomposition theorems, theorems of Cohen-Seidenberg, the normalisation of rings of polynomials, dimension (in the sense of Krull) and characteristic polynomials (in the sense of Hilbert-Samuel)
Cohomologie galoisienne, cours au Collège de France, 1962-1963 by Jean-Pierre Serre( Book )

53 editions published between 1964 and 1986 in 4 languages and held by 735 WorldCat member libraries worldwide

Algebraic groups and class fields : translation of the French edition by Jean-Pierre Serre( Book )

39 editions published between 1959 and 2012 in 4 languages and held by 706 WorldCat member libraries worldwide

Of the Main Results -- Algebraic Curves -- Maps From a Curve to a Commutative Group -- Singular Algebraic Curves -- Generalized Jacobians -- Class Field Theory -- Group Extension and Cohomology -- Bibliography -- Supplementary Bibliography -- Index
Trees by Jean-Pierre Serre( Book )

30 editions published between 1980 and 2013 in English and Undetermined and held by 680 WorldCat member libraries worldwide

The present book is an English translation of "Arbres, Amalgames, SL(2)", published in 1977 by J-P. Serre, and written with the collaboration of H. Bass. The first chapter describes the "arboreal dictionary" between graphs of groups and group actions on trees. The second chapter gives applications to the Bruhat-Tits tree of SL(2) over a local field
Modular functions of one variable V- : proceedings, international conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik, July 2-14, 1976 by International Conference on Modular Functions of One Variable V( Book )

29 editions published in 1977 in 3 languages and held by 494 WorldCat member libraries worldwide

Topics in Galois theory by Jean-Pierre Serre( Book )

26 editions published between 1992 and 2008 in 3 languages and held by 452 WorldCat member libraries worldwide

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for p-groups, p!= 2, as well as Hilbert's irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of
Lectures on the Mordell-Weil theorem by Jean-Pierre Serre( Book )

24 editions published between 1989 and 2013 in English and held by 416 WorldCat member libraries worldwide

This is a translation of "Autour du theoreme de Mordell-Well", a course given by J.-P. Serre at the College de France in 1980 and 1981. These notes were originally written weekly by Michel Waldschmidt and have been reproduced by Publications Mathematiques de l'Universite de Paris VI, by photocopying the handwritten manuscript. The present translation follows roughly the French text, with many modi fications and rearrangements. We have not tried to give a detailed account of the new results due to Faltings, Raynaud, Gross-Zagier ... ; we have just mentioned them in notes at the appropriate places, and given bibliographical references. M.L. Brown Paris, Fall 1988 I.-P. Serre VII CONTENTS 1. Summary. 1 1. 1. Heights. 3 1. 2. The Mordell-Weil theorem and Mordell's conjecture. 3 1. 3. Integral points on algebraic curves. Siegel's theorem. 4 1. 4. Baker's method. 5 1. 5. Hilbert's irreducibility theorem. Sieves. 5 2. Heights. 7 2. 1. The product formula. 7 2. 2. Heights on P m(K). 10 2. 3. Properties of heights. 13 2. 4. Northcott's finiteness theorem. 16 2. 5. Quantitative form of Northcott's theorem. 17 '2. 6. Height associated to a morphism
Local algebra by Jean-Pierre Serre( Book )

16 editions published between 2000 and 2011 in English and held by 392 WorldCat member libraries worldwide

This is an English translation of the now classic "Algèbre Locale - Multiplicités" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Tor-formula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character
Galois groups over Q : proceedings of a workshop held March 23-27, 1987 by Y Ihara( Book )

16 editions published in 1989 in English and Multiple languages and held by 362 WorldCat member libraries worldwide

This volume is the offspring of a week-long workshop on "Galois groups over Q and related topics," which was held at the Mathematical Sciences Research Institute during the week March 23-27, 1987. The organizing committee consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The conference focused on three principal themes: 1. Extensions of Q with finite simple Galois groups. 2. Galois actions on fundamental groups, nilpotent extensions of Q arising from Fermat curves, and the interplay between Gauss sums and cyclotomic units. 3. Representations of Gal(Q/Q) with values in GL(2)j deformations and connections with modular forms. Here is a summary of the conference program: " G. Anderson: "Gauss sums, circular units and the simplex" " G. Anderson and Y. Ihara: "Galois actions on 11"1 (" ") and higher circular units" " D. Blasius: "Maass forms and Galois representations" " P. Deligne: "Galois action on 1I"1(P-{0, 1, oo}) and Hodge analogue" " W. Feit: "Some Galois groups over number fields" " Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})"--Survey talk " U. Jannsen: "Galois cohomology of i-adic representations" " B. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" " B. Mazur: "Deforming GL(2) Galois representations" " K. Ribet: "Lowering the level of modular representations of Gal(Q/ Q)" " J-P. Serre: - Introductory Lecture - "Degree 2 modular representations of Gal(Q/Q)" " J
Oeuvres = Collected papers by Jean-Pierre Serre( Book )

23 editions published between 1986 and 2013 in 3 languages and held by 352 WorldCat member libraries worldwide

Grothendieck-Serre correspondence by A Grothendieck( Book )

25 editions published between 2001 and 2004 in 3 languages and held by 346 WorldCat member libraries worldwide

"The book is a bilingual (French and English) edition of the mathematical correspondence between A. Grothendieck and J.-P. Serre. The original French text of 84 letters is supplemented here by the English translation, with French text printed on the left-hand pages and the corresponding English text printed on the right-hand pages. The book also includes several facsimiles of original letters." "The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schernes, Riemann-Roch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.) Also included are a few letters written between 1984 and 1987. The letters are supplemented by J.-P. Serre's notes, which give explanations, corrections, and references further results." "The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created."--BOOK JACKET
Abelian l̳-adic representations and elliptic curves; McGill University lecture notes by Jean-Pierre Serre( Book )

5 editions published in 1968 in English and held by 329 WorldCat member libraries worldwide

Gesammelte Abhandlungen by Ferdinand Georg Frobenius( Book )

18 editions published between 1968 and 2015 in 3 languages and held by 325 WorldCat member libraries worldwide

Abelian l-adic representations and elliptic curves by Jean-Pierre Serre( Book )

32 editions published between 1968 and 1998 in 3 languages and held by 307 WorldCat member libraries worldwide

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one finds a nice correspondence between the l-adic representations and the linear representations of some algebraic groups (now called Taniyama groups) The last chapter handles the case of elliptic curves with no complex multiplication, the main result of which is that the image of the Galois group (in the corresponding l-adic representation) is "large."
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WorldCat IdentitiesRelated Identities
A course in arithmetic
A course in arithmeticAlgèbres de Lie semi-simples complexesLocal fieldsLie algebras and Lie groups; 1964 lectures given at Harvard UniversityGalois cohomologyAlgèbre locale, multiplicités; cours au Collège de France, 1957-1958Algebraic groups and class fields : translation of the French editionTrees
Alternative Names
Jean-Pierre Serre Frans wiskundige

Jean-Pierre Serre fransk matematikar

Jean-Pierre Serre fransk matematiker

Jean-Pierre Serre französischer Mathematiker

Jean-Pierre Serre French mathematician

Jean-Pierre Serre matemàtic francès

Jean-Pierre Serre matematician francez

Jean-Pierre Serre matematico e accademico francese

Jean-Pierre Serre matemático francés

Jean-Pierre Serre matemáticu francés

Jean-Pierre Serre matematik a topolog

Jean-Pierre Serre matematyk francuski

Jean-Pierre Serre mathématicien français

Serr, Ž.

Serr, Ž. 1926-

Serr, Ž.-P.

Serr, Z.-P. 1926-

Serr, Zh.-P.

Serr, Zh.-P. 1926-

Serr, Zhan-Pʹer 1926-

Serre, J.

Serre, J. 1926-

Serre, J.P.

Serre, J.-P. 1926-

Serre, J. P. (Jean Pierre), 1926-

Serre, Jean 1926-

Serre, Jean P. 1926-

Serre, Jean-Pierre

Serre, Jean-Pierre 1926-

Жан-Пьер Серр французский математик

Жан-П'єр Серр

Серр, Ж.-П..

Серр, Ж.-П 1926-

ז'אן-פייר סר

ז'אן-פייר סר מתמטיקאי צרפתי

جان-بيير سير

جان-بيير سير رياضياتي فرنسي

جان-پیری سیری

ژان پیر سر ریاضی‌دان فرانسوی

ژان-پی‌یر سر

ရောန်-ဖြဲ ဆဲ

장피에르 세르


セール, J.-P.

セール, ジャンーピエール


讓-皮埃爾·塞爾 法國數學家