Stacks Project Expository Collection
Stacks Project Expository Collection
Wei Ho, University of Michigan, Ann Arbor
Aise Johan de Jong, Columbia University, New York
The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.
- Brings researchers up to speed with recent developments in the geometry of algebraic spaces and algebraic stacks
- Presents many classical results using a modern language and using modern techniques
- Many steps in proofs usually left implicit or to the reader are backed up with ample references to the Stacks project
Product details
No date availablePaperback
9781009054850
250 pages
228 × 152 × 18 mm
0.46kg
Table of Contents
- List of contributors
- Preface
- 1. Projectivity of the moduli of curves Raymond Cheng, Carl Lian and Takumi Murayama
- 2. The stack of admissible covers is algebraic Elsa Corniani, Neeraj Deshmukh, Brett Nasserden, Emanuel Reinecke, Nawaz Sultani and Rachel Webb
- 3. Projectivity of the moduli space of vector bundles on a curve Jarod Alper, Pieter Belmans, Daniel Bragg, Jason Liang and Tuomas Tajakka
- 4. Boundedness of semistable sheaves Haoyang Guo, Sanal Shivaprasad, Dylan Spence and Yueqiao Wu
- 5. Theorem of the Base Raymond Cheng, Lena Ji, Matt Larson and Noah Olander
- 6. Weil restriction for schemes and beyond Lena Ji, Shizhang Li, Patrick McFaddin, Drew Moore and Matthew Stevenson
- 7. Heights over finitely generated fields Stephen McKean and Soumya Sankar
- 8. An explicit self-duality Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte and Kirsten Wickelgren
- 9. Tannakian reconstruction of coalgebroids Yifei Zhao.
