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| Author | : V. E. Voskresenskii |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 234 |
| Release | : 2011-10-06 |
| Genre | : Mathematics |
| ISBN | : 0821872885 |
Download Algebraic Groups and Their Birational Invariants Book in PDF, ePub and Kindle
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.
| Author | : Valentin Evgenʹevich Voskresenskiĭ |
| Publisher | : |
| Total Pages | : 234 |
| Release | : 1998 |
| Genre | : Geometry, Algebraic |
| ISBN | : 9781470416225 |
Download Algebraic Groups and Their Birational Invariants Book in PDF, ePub and Kindle
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.
| Author | : Walter Ricardo Ferrer Santos |
| Publisher | : CRC Press |
| Total Pages | : 479 |
| Release | : 2017-09-19 |
| Genre | : Mathematics |
| ISBN | : 1482239167 |
Download Actions and Invariants of Algebraic Groups Book in PDF, ePub and Kindle
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.
| Author | : Gus Lehrer |
| Publisher | : Cambridge University Press |
| Total Pages | : 396 |
| Release | : 1997-01-23 |
| Genre | : Mathematics |
| ISBN | : 9780521585323 |
Download Algebraic Groups and Lie Groups Book in PDF, ePub and Kindle
This volume contains original research articles by many of the world's leading researchers in algebraic and Lie groups. Its inclination is algebraic and geometic, although analytical aspects are included. The central theme reflects the interests of R. W. Richardson, viz connections between representation theory and the structure and geometry of algebraic groups. All workers on algebraic and Lie groups will find that this book contains a wealth of interesting material.
| Author | : Walter Ricardo Ferrer Santos |
| Publisher | : |
| Total Pages | : 472 |
| Release | : 2017 |
| Genre | : Affine algebraic groups |
| ISBN | : 9780429135736 |
Download Actions and Invariants of Algebraic Groups, Second Edition Book in PDF, ePub and Kindle
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.
| Author | : Mahir Bilen Can |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 306 |
| Release | : 2017-04-06 |
| Genre | : Mathematics |
| ISBN | : 1470426013 |
Download Algebraic Groups: Structure and Actions Book in PDF, ePub and Kindle
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.
| Author | : J. S. Milne |
| Publisher | : Cambridge University Press |
| Total Pages | : 665 |
| Release | : 2017-09-21 |
| Genre | : Mathematics |
| ISBN | : 1316739155 |
Download Algebraic Groups Book in PDF, ePub and Kindle
Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the Barsotti–Chevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the Borel–Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.
| Author | : Martin Lorenz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 200 |
| Release | : 2005-03-10 |
| Genre | : Mathematics |
| ISBN | : 9783540243236 |
Download Multiplicative Invariant Theory Book in PDF, ePub and Kindle
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.
| Author | : Vladimir Platonov |
| Publisher | : Cambridge University Press |
| Total Pages | : 379 |
| Release | : 2023-08-31 |
| Genre | : Mathematics |
| ISBN | : 052111361X |
Download Algebraic Groups and Number Theory Book in PDF, ePub and Kindle
The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.
| Author | : William Joseph Haboush |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 429 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821815415 |
Download Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional Methods Book in PDF, ePub and Kindle
Proceedings of a research institute held at Pennsylvania State University, July 1991, focusing on quantum and infinite-dimensional methods of algebraic groups. Topics include perverse sheaves, finite Chevalley groups, the general theory of algebraic groups, representations, invariant theory, general
