Tignol, JeanPierre
Overview
Works:  57 works in 176 publications in 2 languages and 3,846 library holdings 

Genres:  History Conference papers and proceedings 
Roles:  Author, Editor, Opponent, 956, Thesis advisor 
Publication Timeline
.
Most widely held works by
JeanPierre Tignol
Galois' theory of algebraic equations by
JeanPierre Tignol(
Book
)
57 editions published between 1980 and 2016 in English and French and held by 1,422 WorldCat member libraries worldwide
"The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as 'group' and 'field'. A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory"
57 editions published between 1980 and 2016 in English and French and held by 1,422 WorldCat member libraries worldwide
"The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as 'group' and 'field'. A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory"
Algebra and number theory : proceedings of a conference held in Fez, Morocco(
)
15 editions published between 1999 and 2000 in English and held by 1,204 WorldCat member libraries worldwide
"This comprehensive reference demonstrates the key manipulations surrounding Brauer groups, graded rings, group representations, ideal classes of number fields, padic differential equations, and rationality problems of invariant fields  displaying an extraordinary command of the most advanced methods in current algebra."BOOK JACKET. "Containing over 300 references, Algebra and Number Theory is an ideal resource for pure and applied mathematicians, algebraists, number theorists, and upperlevel undergraduate and graduate students in these disciplines."BOOK JACKET
15 editions published between 1999 and 2000 in English and held by 1,204 WorldCat member libraries worldwide
"This comprehensive reference demonstrates the key manipulations surrounding Brauer groups, graded rings, group representations, ideal classes of number fields, padic differential equations, and rationality problems of invariant fields  displaying an extraordinary command of the most advanced methods in current algebra."BOOK JACKET. "Containing over 300 references, Algebra and Number Theory is an ideal resource for pure and applied mathematicians, algebraists, number theorists, and upperlevel undergraduate and graduate students in these disciplines."BOOK JACKET
Geometric methods in the algebraic theory of quadratic forms : summer school, Lens, 2000 by
Oleg T Izhboldin(
Book
)
21 editions published in 2004 in English and held by 478 WorldCat member libraries worldwide
The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes  an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions;  papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension;  a contribution in French by Bruno Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties. Most of the material appears here for the first time in print. The intended audience consists of research mathematicians at the graduate or postgraduate level
21 editions published in 2004 in English and held by 478 WorldCat member libraries worldwide
The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes  an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions;  papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension;  a contribution in French by Bruno Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties. Most of the material appears here for the first time in print. The intended audience consists of research mathematicians at the graduate or postgraduate level
The book of involutions by
MaxAlbert Knus(
Book
)
1 edition published in 1998 in English and held by 313 WorldCat member libraries worldwide
This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebratheoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type F₄ or G₂ arising from exceptional Jordan or composition algebras
1 edition published in 1998 in English and held by 313 WorldCat member libraries worldwide
This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebratheoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type F₄ or G₂ arising from exceptional Jordan or composition algebras
Value functions on simple algebras, and associated graded rings by
JeanPierre Tignol(
)
14 editions published between 2015 and 2016 in English and held by 284 WorldCat member libraries worldwide
This monograph is the first booklength treatment of valuation theory on finitedimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of noncrossed products and Platonov's solution of the TannakaArtin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians
14 editions published between 2015 and 2016 in English and held by 284 WorldCat member libraries worldwide
This monograph is the first booklength treatment of valuation theory on finitedimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of noncrossed products and Platonov's solution of the TannakaArtin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians
Œuvres = collected works by
Jacques Tits(
Book
)
4 editions published in 2013 in 3 languages and held by 47 WorldCat member libraries worldwide
4 editions published in 2013 in 3 languages and held by 47 WorldCat member libraries worldwide
Oeuvres. Collected works by
Jacques Tits(
Book
)
1 edition published in 2013 in French and held by 15 WorldCat member libraries worldwide
1 edition published in 2013 in French and held by 15 WorldCat member libraries worldwide
Critical sets in 3space. Biquaternion algebras and quartic extensions / by Tsit Yuen Lam, David B. Leep and JeanPierre Tignol
[u.a.] by
Matthew Grayson(
Book
)
1 edition published in 1993 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 5 WorldCat member libraries worldwide
Algebra and number theory by
M'hammed Boulagouaz(
)
5 editions published between 1999 and 2000 in English and held by 5 WorldCat member libraries worldwide
Annotation
5 editions published between 1999 and 2000 in English and held by 5 WorldCat member libraries worldwide
Annotation
Oeuvres. ollected works by
Jacques Tits(
)
1 edition published in 2013 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 2013 in French and held by 5 WorldCat member libraries worldwide
Décomposition et descente de produits tensoriels d'algèbres de quaternions by
JeanPierre Tignol(
Book
)
3 editions published in 1978 in French and Undetermined and held by 5 WorldCat member libraries worldwide
3 editions published in 1978 in French and Undetermined and held by 5 WorldCat member libraries worldwide
Galois' Theory Of Algebraic Equations (Second Edition) by
JeanPierre Tignol(
)
1 edition published in 2015 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 4 WorldCat member libraries worldwide
Introduzione all'aritmetica delle algebre di quaternioni ; Metodi di simulazione, meccanica stocastica, teoria dei grafi e
applicazioni ; Teoria dei quanti : fondamenti e problemi attuali(
Book
)
1 edition published in 1991 in French and held by 3 WorldCat member libraries worldwide
1 edition published in 1991 in French and held by 3 WorldCat member libraries worldwide
Un complexe de groupes abéliens associé à une extension abélienne finie déxposant 2 de corps commutatifs by
JeanPierre Tignol(
Book
)
2 editions published in 1979 in French and held by 3 WorldCat member libraries worldwide
2 editions published in 1979 in French and held by 3 WorldCat member libraries worldwide
Applications de la descente quadratique des algèbres simples à l'étude de la structure des corps à involution by
JeanPierre Tignol(
Book
)
2 editions published in 1977 in French and held by 3 WorldCat member libraries worldwide
2 editions published in 1977 in French and held by 3 WorldCat member libraries worldwide
Involutions and trace forms on exterior powers of a central simple algebra by R. Skip Garibaldi(
Book
)
3 editions published between 2000 and 2001 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 2000 and 2001 in English and held by 3 WorldCat member libraries worldwide
Critical sets in 3space by
Matthew Grayson(
Book
)
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
Discriminant and Clifford algebras by
Anne QuéguinerMathieu(
Book
)
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
Graded Hermitian forms and Springer's theorem by J.F Renard(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
Algebre by
JeanPierre Tignol(
Book
)
1 edition published in 1988 in French and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in French and held by 2 WorldCat member libraries worldwide
more
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Audience Level
0 

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Kids  General  Special 
Related Identities
 Boulagouaz, M'hammed 1955 Author Editor
 Izhboldin, Oleg T. (Oleg Tomovich) 19632000 Author
 Blyth, T. S. (Thomas Scott) Editor
 Rost, Markus
 Merkurjev, Alexander 1955
 Knus, MaxAlbert Author
 Wadsworth, Adrian R. 1947
 Buekenhout, Francis Author Editor
 Maldeghem, H. van Editor
 Mühlherr, Bernhard Matthias Editor
Associated Subjects
Abelian groups Algebra Algebraic fields Associative rings Compact spaces Critical point theory (Mathematical analysis) Equations, Theory of Field theory (Physics) Forms, Pfister Forms, Quadratic Galois theory Geometry, Algebraic Group theory Hermitian forms Homology theory Linear algebraic groups Mathematics Number theory Quaternions Rings (Algebra) Tensor products Theory of descent (Mathematics) Valuation theory