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OverviewThis 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. Full Product DetailsAuthor: Martin OlssonPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.700kg ISBN: 9781470427986ISBN 10: 1470427982 Pages: 298 Publication Date: 30 May 2016 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Summary of background material Grothendieck topologies and sites Fibered categories Descent and the stack condition Algebraic spaces Invariants and quotients Quasi-coherent sheaves on algebraic spaces Algebraic stacks: Definitions and basic properties Quasi-coherent sheaves on algebraic stacks Basic geometric properties and constructions for stacks Coarse moduli spaces Gerbes Moduli of curves Glossary of category theory Bibliography Index of notation Index of terminologyReviewsIt 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 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 Graduate students will benefit from the self-contained and accessible presentation of the entire theory, as well as the numerous exercises. Researchers will like the comprehensive, up-to-date treatment of foundations and key results, together with detailed proofs. Summing up, this is an excellent monograph that fills a large gap in the literature. -Stefan Schroer, Mathematical Reviews Author InformationMartin Olsson, University of California, Berkeley, CA, USA. Tab Content 6Author Website:Countries AvailableAll regions |
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