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.
Rezensionen / Stimmen
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 Schroeer, Mathematical Reviews
Reihe
Sprache
Verlagsort
Zielgruppe
Maße
Höhe: 254 mm
Breite: 178 mm
Gewicht
ISBN-13
978-1-4704-2798-6 (9781470427986)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Martin Olsson, University of California, Berkeley, CA, USA.
Introduction
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 terminology
