TY  - BOOK
AU  - Olsson,Martin
TI  - Algebraic spaces and stacks
T2  - American Mathematical Society colloquium publications
SN  - 9781470427986 (alk. paper)
U1  - 516.35 23
PY  - 2016///
CY  - Providence : 
PB  - American Mathematical Society
KW  - Algebraic spaces
KW  - Algebraic stacks
N1  - Includes bibliographical references and index; Introduction --
1. Summary of background material --
2. Grothendieck topologies and sites --
3. Fibered categories --
4. Descent and the stack condition --
5. Algebraic spaces --
6. Invariants and quotients --
7. Quasi-coherent sheaves on algebraic spaces --
8. Algebraic stacks: Definitions and basic properties --
9. Quasi-coherent sheaves on algebraic stacks --
10. Basic geometric properties and constructions for stacks --
11. Coarse moduli spaces --
12. Gerbes --
13.  Moduli of curves --
Appendix A. Glossary of category theory --
Bibliography --
Index of notation --
Index of terminology
N2  - 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 curv
ER  -