Algebraic spaces and stacks / Martin Olsson.
Material type:
TextSeries: American Mathematical Society colloquium publications ; v 62.Publication details: Providence : American Mathematical Society, ©2016.Description: xi, 298 pages : illustrations ; 26 cmISBN: - 9781470427986 (alk. paper)
- 516.35 23 Ol52
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 516.35 Ol52 (Browse shelf(Opens below)) | Available | 137738 |
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| 516.35 Od22 lectures on torus embeddings and applications | 516.35 Od22 Convex bodies and algebraic geometry | 516.35 Ol52 Algebraic goemetry | 516.35 Ol52 Algebraic spaces and stacks / | 516.35 Oy98 Non-commutative algebraic geometry | 516.35 P189 Fixed point index as a local Lefschetz number | 516.35 P266 Algebraic geometry V |
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.
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.
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