Algebraic spaces and stacks
Material type:
TextLanguage: English Series: American Mathematical Society colloquium publications ; volume 62Publication details: Rhode Island : American Mathematical Society, 2016 Description: xi, 298p. : illustrations ; 26 cmISBN: 9781470474805Subject(s): Algebraic spaces | Algebraic stacks | Algebraic geometry -- Foundations -- Generalizations (algebraic spaces, stacks) | Algebraic geometry -- Families, fibrations -- Stacks and moduli problems | Algebraic geometry -- Families, fibrations -- Fine and coarse moduli spacesDDC classification: 514.74 Online resources: Table of Contents | Reviews Summary: 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
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Book
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SMS Library | 514.74 OLS-A (Browse shelf(Opens below)) | Available | 25202 |
Includes bibliographical references (pages 291-293) and index.
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.
Graduate students and research mathematicians interested in algebraic spaces and stacks.
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