Algebraic Spaces PDF Download
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Author | : Martin Olsson |
Publisher | : American Mathematical Society |
Total Pages | : 313 |
Release | : 2023-09-15 |
Genre | : Mathematics |
ISBN | : 1470474808 |
Download Algebraic Spaces and Stacks Book in PDF, ePub and Kindle
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix. It is splendid to have a self-contained treatment of stacks, written by a leading practitioner. Finally we have a reference where one can find careful statements and proofs of many of the foundational facts in this important subject. Researchers and students at all levels will be grateful to Olsson for writing this book. —William Fulton, University of Michigan This is a carefully planned out book starting with foundations and ending with detailed proofs of key results in the theory of algebraic stacks. —Johan de Jong, Columbia University
Author | : Donald Knutson |
Publisher | : Springer |
Total Pages | : 267 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540366636 |
Download Algebraic Spaces Book in PDF, ePub and Kindle
Author | : Martin Olsson |
Publisher | : American Mathematical Soc. |
Total Pages | : 313 |
Release | : 2016-05-13 |
Genre | : Mathematics |
ISBN | : 1470427982 |
Download Algebraic Spaces and Stacks Book in PDF, ePub and Kindle
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
Author | : Michael Artin |
Publisher | : |
Total Pages | : 39 |
Release | : 1971 |
Genre | : Algebraic functions |
ISBN | : 9780300013962 |
Download Algebraic Spaces Book in PDF, ePub and Kindle
Author | : Frank D. Grosshans |
Publisher | : Springer |
Total Pages | : 158 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540696172 |
Download Algebraic Homogeneous Spaces and Invariant Theory Book in PDF, ePub and Kindle
The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.
Author | : Jonathan A. Barmak |
Publisher | : Springer Science & Business Media |
Total Pages | : 184 |
Release | : 2011-08-24 |
Genre | : Mathematics |
ISBN | : 3642220029 |
Download Algebraic Topology of Finite Topological Spaces and Applications Book in PDF, ePub and Kindle
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Author | : Martin Olsson |
Publisher | : American Mathematical Society |
Total Pages | : 313 |
Release | : 2023-09-15 |
Genre | : Mathematics |
ISBN | : 1470474808 |
Download Algebraic Spaces and Stacks Book in PDF, ePub and Kindle
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix. It is splendid to have a self-contained treatment of stacks, written by a leading practitioner. Finally we have a reference where one can find careful statements and proofs of many of the foundational facts in this important subject. Researchers and students at all levels will be grateful to Olsson for writing this book. —William Fulton, University of Michigan This is a carefully planned out book starting with foundations and ending with detailed proofs of key results in the theory of algebraic stacks. —Johan de Jong, Columbia University
Author | : Francois Bergeron |
Publisher | : CRC Press |
Total Pages | : 227 |
Release | : 2009-07-06 |
Genre | : Mathematics |
ISBN | : 1439865078 |
Download Algebraic Combinatorics and Coinvariant Spaces Book in PDF, ePub and Kindle
Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and
Author | : J. M. Boardman |
Publisher | : Springer |
Total Pages | : 268 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540377999 |
Download Homotopy Invariant Algebraic Structures on Topological Spaces Book in PDF, ePub and Kindle
Author | : Maxim E. Kazaryan |
Publisher | : Springer |
Total Pages | : 231 |
Release | : 2019-01-21 |
Genre | : Mathematics |
ISBN | : 3030029433 |
Download Algebraic Curves Book in PDF, ePub and Kindle
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework