Download book Algebraic Spaces and Stacks

Download book Algebraic Spaces and Stacks

Algebraic Spaces and Stacks by Martin Olsson
Algebraic Spaces and Stacks
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Author: Martin Olsson
Page Count: 299 pages
Published Date: 30 May 2016
Publisher: American Mathematical Society
Publication Country: Providence, United States
Language: English
ISBN: 9781470427986
File size: 9 Mb
File Name: Algebraic.Spaces.and.Stacks.pdf
Download Link: Algebraic Spaces and Stacks
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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.

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