Stacks Project Expository Collection

A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.

Pieter Belmans (Edited by), Wei Ho (Edited by), Aise Johan de Jong (Edited by)

9781009054850, Cambridge University Press

Paperback / softback, published 27 October 2022

250 pages
22.8 x 15.2 x 1.8 cm, 0.46 kg

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.

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.

Subject Areas: Geometry [PBM]