Algebraic Groups and Their Birational Invariants

Algebraic Groups and Their Birational Invariants

Author: V. E. Voskresenskii

Publisher: American Mathematical Soc.

Published: 2011-10-06

Total Pages: 234

ISBN-13: 0821872885

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Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.


Book Synopsis Algebraic Groups and Their Birational Invariants by : V. E. Voskresenskii

Download or read book Algebraic Groups and Their Birational Invariants written by V. E. Voskresenskii and published by American Mathematical Soc.. This book was released on 2011-10-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

Algebraic Groups and Their Birational Invariants

Algebraic Groups and Their Birational Invariants

Author: Valentin Evgenʹevich Voskresenskiĭ

Publisher:

Published: 1998

Total Pages: 234

ISBN-13: 9781470416225

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Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, R-equivalence, projective toric varieties, invariants.


Book Synopsis Algebraic Groups and Their Birational Invariants by : Valentin Evgenʹevich Voskresenskiĭ

Download or read book Algebraic Groups and Their Birational Invariants written by Valentin Evgenʹevich Voskresenskiĭ and published by . This book was released on 1998 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, R-equivalence, projective toric varieties, invariants.

Actions and Invariants of Algebraic Groups

Actions and Invariants of Algebraic Groups

Author: Walter Ricardo Ferrer Santos

Publisher: CRC Press

Published: 2017-09-19

Total Pages: 542

ISBN-13: 1351644777

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Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.


Book Synopsis Actions and Invariants of Algebraic Groups by : Walter Ricardo Ferrer Santos

Download or read book Actions and Invariants of Algebraic Groups written by Walter Ricardo Ferrer Santos and published by CRC Press. This book was released on 2017-09-19 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.

Actions and Invariants of Algebraic Groups, Second Edition

Actions and Invariants of Algebraic Groups, Second Edition

Author: Walter Ricardo Ferrer Santos

Publisher:

Published: 2017

Total Pages: 472

ISBN-13: 9780429135736

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Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions. Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.--Provided by publisher.


Book Synopsis Actions and Invariants of Algebraic Groups, Second Edition by : Walter Ricardo Ferrer Santos

Download or read book Actions and Invariants of Algebraic Groups, Second Edition written by Walter Ricardo Ferrer Santos and published by . This book was released on 2017 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions. Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.--Provided by publisher.

Galois Theory, Rings, Algebraic Groups and Their Applications

Galois Theory, Rings, Algebraic Groups and Their Applications

Author: Simeon Ivanov

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 290

ISBN-13: 9780821831403

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This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.


Book Synopsis Galois Theory, Rings, Algebraic Groups and Their Applications by : Simeon Ivanov

Download or read book Galois Theory, Rings, Algebraic Groups and Their Applications written by Simeon Ivanov and published by American Mathematical Soc.. This book was released on 1992 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.

Algebraic Groups: Structure and Actions

Algebraic Groups: Structure and Actions

Author: Mahir Bilen Can

Publisher: American Mathematical Soc.

Published: 2017-04-06

Total Pages: 294

ISBN-13: 1470426013

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This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane University, New Orleans, Louisiana. This volume consists of six articles on algebraic groups, including an enhanced exposition of the classical results of Chevalley and Rosenlicht on the structure of algebraic groups; an enhanced survey of the recently developed theory of pseudo-reductive groups; and an exposition of the recently developed operational -theory for singular varieties. In addition, there are three research articles containing previously unpublished foundational results on birational automorphism groups of algebraic varieties; solution of Hermite-Joubert problem over -closed fields; and cohomological invariants and applications to classifying spaces. The old and new results presented in these articles will hopefully become cornerstones for the future development of the theory of algebraic groups and applications. Graduate students and researchers working in the fields of algebraic geometry, number theory, and representation theory will benefit from this unique and broad compilation of fundamental results on algebraic group theory.


Book Synopsis Algebraic Groups: Structure and Actions by : Mahir Bilen Can

Download or read book Algebraic Groups: Structure and Actions written by Mahir Bilen Can and published by American Mathematical Soc.. This book was released on 2017-04-06 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane University, New Orleans, Louisiana. This volume consists of six articles on algebraic groups, including an enhanced exposition of the classical results of Chevalley and Rosenlicht on the structure of algebraic groups; an enhanced survey of the recently developed theory of pseudo-reductive groups; and an exposition of the recently developed operational -theory for singular varieties. In addition, there are three research articles containing previously unpublished foundational results on birational automorphism groups of algebraic varieties; solution of Hermite-Joubert problem over -closed fields; and cohomological invariants and applications to classifying spaces. The old and new results presented in these articles will hopefully become cornerstones for the future development of the theory of algebraic groups and applications. Graduate students and researchers working in the fields of algebraic geometry, number theory, and representation theory will benefit from this unique and broad compilation of fundamental results on algebraic group theory.

Algebraic Groups

Algebraic Groups

Author: J. S. Milne

Publisher: Cambridge University Press

Published: 2017-09-21

Total Pages: 665

ISBN-13: 1107167485

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


Book Synopsis Algebraic Groups by : J. S. Milne

Download or read book Algebraic Groups written by J. S. Milne and published by Cambridge University Press. This book was released on 2017-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Multiplicative Invariant Theory

Multiplicative Invariant Theory

Author: Martin Lorenz

Publisher: Springer Science & Business Media

Published: 2005-03-10

Total Pages: 200

ISBN-13: 9783540243236

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Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.


Book Synopsis Multiplicative Invariant Theory by : Martin Lorenz

Download or read book Multiplicative Invariant Theory written by Martin Lorenz and published by Springer Science & Business Media. This book was released on 2005-03-10 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.

Algebraic Groups and Number Theory

Algebraic Groups and Number Theory

Author: Vladimir Platonov

Publisher: Cambridge University Press

Published: 2023-08-31

Total Pages: 379

ISBN-13: 052111361X

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The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.


Book Synopsis Algebraic Groups and Number Theory by : Vladimir Platonov

Download or read book Algebraic Groups and Number Theory written by Vladimir Platonov and published by Cambridge University Press. This book was released on 2023-08-31 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

Algebraic Groups and Their Generalizations: Classical Methods

Algebraic Groups and Their Generalizations: Classical Methods

Author: William Joseph Haboush

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 397

ISBN-13: 0821815407

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Book Synopsis Algebraic Groups and Their Generalizations: Classical Methods by : William Joseph Haboush

Download or read book Algebraic Groups and Their Generalizations: Classical Methods written by William Joseph Haboush and published by American Mathematical Soc.. This book was released on 1994 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: