Merkurjev, Alexander 1955
Overview
Works:  12 works in 32 publications in 3 languages and 953 library holdings 

Roles:  Author, 958, Other 
Publication Timeline
.
Most widely held works by
Alexander Merkurjev
The algebraic and geometric theory of quadratic forms by
Richard S Elman(
Book
)
10 editions published in 2008 in English and held by 328 WorldCat member libraries worldwide
This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages
10 editions published in 2008 in English and held by 328 WorldCat member libraries worldwide
This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages
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
Cohomological invariants in Galois cohomology by
Skip Garibaldi(
Book
)
10 editions published in 2003 in English and held by 273 WorldCat member libraries worldwide
"This volume is concerned with algebraic invariants, such as the StiefelWhitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of etale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the HasseWitt invariant of quadratic forms." "The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of Gtorsors with values in H[superscript 3](Q/Z(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant."Jacket
10 editions published in 2003 in English and held by 273 WorldCat member libraries worldwide
"This volume is concerned with algebraic invariants, such as the StiefelWhitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of etale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the HasseWitt invariant of quadratic forms." "The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of Gtorsors with values in H[superscript 3](Q/Z(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant."Jacket
Algebra by
John W Milnor(
Book
)
1 edition published in 2010 in English and held by 18 WorldCat member libraries worldwide
1 edition published in 2010 in English and held by 18 WorldCat member libraries worldwide
A list of index reduction formulas by
Alexander Merkurjev(
Book
)
2 editions published in 1994 in German and English and held by 8 WorldCat member libraries worldwide
2 editions published in 1994 in German and English and held by 8 WorldCat member libraries worldwide
Requivalence and special unitary groups by
V Černusov(
Book
)
2 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
On standard norm varieties by
Nikita Karpenko(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Variétés rationnelles et torseurs sous les groupes linéaires : obstruction de BrauerManin pour les points entiers et invariants
cohomologiques supérieurs by
Yang Cao(
)
1 edition published in 2017 in French and held by 1 WorldCat member library worldwide
Dans cette thèse, on s'intéresse à des propriétés arithmétiques des variétés algébriques. Elle contient deux parties : partie géométrique (sur un corps quelconque) et partie arithmétique (sur un corps de nombres). Dans la partie géométrique, j'étudie le quotient par sa partie constante du troisième groupe de cohomologie non ramifiée des surfaces (géométriquement) rationnelles et de leurs torseurs universels. Pour les surfaces de del Pezzo de degré au moins 5, je montre que ce quotient est trivial, sauf pour des surfaces de del Pezzo de degré 8 d'un type particulier. Pour les torseurs universels cidessus, je montre que ce quotient est fini et je donne une condition suffisante pour qu'il soit nul, en termes de la structure galoisienne du groupe de Picard géométrique de la surface. Dans la partie arithmétique, on étudie l'obstruction de BrauerManin à l'approximation forte. En collaboration avec C. Demarche et F. Xu, nous établissons l'équivalence de l'obstruction de BrauerManin étale et de l'obstruction de descente pour les variétés quasiprojectives. Ensuite, j'établis un théorème très général sur l'approximation forte pour les variétés ouvertes munies d'une action d'un groupe linéaire connexe G et dont un ouvert est un espace homogène de G
1 edition published in 2017 in French and held by 1 WorldCat member library worldwide
Dans cette thèse, on s'intéresse à des propriétés arithmétiques des variétés algébriques. Elle contient deux parties : partie géométrique (sur un corps quelconque) et partie arithmétique (sur un corps de nombres). Dans la partie géométrique, j'étudie le quotient par sa partie constante du troisième groupe de cohomologie non ramifiée des surfaces (géométriquement) rationnelles et de leurs torseurs universels. Pour les surfaces de del Pezzo de degré au moins 5, je montre que ce quotient est trivial, sauf pour des surfaces de del Pezzo de degré 8 d'un type particulier. Pour les torseurs universels cidessus, je montre que ce quotient est fini et je donne une condition suffisante pour qu'il soit nul, en termes de la structure galoisienne du groupe de Picard géométrique de la surface. Dans la partie arithmétique, on étudie l'obstruction de BrauerManin à l'approximation forte. En collaboration avec C. Demarche et F. Xu, nous établissons l'équivalence de l'obstruction de BrauerManin étale et de l'obstruction de descente pour les variétés quasiprojectives. Ensuite, j'établis un théorème très général sur l'approximation forte pour les variétés ouvertes munies d'une action d'un groupe linéaire connexe G et dont un ouvert est un espace homogène de G
Requivalence in spinor groups by
Vladimir I Černusov(
Book
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Requivalence and special unitary groups by V Chernousov(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
A Collection of Manuscripts Written in Honour of Alexander S. Merkurjev on the Occasion of His Sixtieth Birthday(
Book
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
Cohomological invariants in Galois theory by
Skip Garibaldi(
Book
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
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Alexander Merkurjev Amerikaans wiskundige
Alexander Merkurjev amerikansk matematikar
Alexander Merkurjev amerikansk matematiker
Alexander Merkurjev matemático estadounidense
Alexander Merkurjev matematico statunitense
Alexander Merkurjev mathématicien américain
Alexander Merkurjev USamerikanischer Mathematiker
Merkurjev, A.
Merkurjev, Alexander
Merkurjev, Alexandr, 1955
Александр Меркурьев советский и американский математик
אלכסנדר מרקורייב מתמטיקאי אמריקאי
アレクサンドル・メルクリエフ
亚历山大·麦克尔耶夫
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