Algebraic Spaces and Stacks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Spaces and Stacks write by Martin Olsson. This book was released on 2016-05-13. Algebraic Spaces and Stacks available 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.
Algebraic Spaces and Stacks
Algebraic Spaces and Stacks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Spaces and Stacks write by Martin Olsson. This book was released on 2023-09-15. Algebraic Spaces and Stacks available 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
Fundamental Algebraic Geometry
Fundamental Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fundamental Algebraic Geometry write by Barbara Fantechi. This book was released on 2005. Fundamental Algebraic Geometry available in PDF, EPUB and Kindle. Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
European Congress of Mathematics
European Congress of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook European Congress of Mathematics write by Carles Casacuberta. This book was released on 2012-12-06. European Congress of Mathematics available in PDF, EPUB and Kindle. This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
Homotopical Algebraic Geometry II: Geometric Stacks and Applications
Homotopical Algebraic Geometry II: Geometric Stacks and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Homotopical Algebraic Geometry II: Geometric Stacks and Applications write by Bertrand Toën. This book was released on 2008. Homotopical Algebraic Geometry II: Geometric Stacks and Applications available in PDF, EPUB and Kindle. This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.
