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Stacks Project Expository Collection

£95.00

Part of London Mathematical Society Lecture Note Series

Raymond Cheng, Carl Lian, Takumi Murayama, Elsa Corniani, Neeraj Deshmukh, Brett Nasserden, Emanuel Reinecke, Nawaz Sultani, Rachel Webb, Jarod Alper, Pieter Belmans, Daniel Bragg, Jason Liang, Tuomas Tajakka, Haoyang Guo, Sanal Shivaprasad, Dylan Spence, Yueqiao Wu, Lena Ji, Matt Larson, Noah Olander, Shizhang Li, Patrick McFaddin, Drew Moore, Matthew Stevenson, Stephen McKean, Soumya Sankar, Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte, Kirsten Wickelgren, Yifei Zhao
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  • Date Published: October 2022
  • availability: Available
  • format: Paperback
  • isbn: 9781009054850

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About the Authors
  • 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
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    Product details

    • Date Published: October 2022
    • format: Paperback
    • isbn: 9781009054850
    • length: 250 pages
    • dimensions: 228 x 152 x 18 mm
    • weight: 0.46kg
    • availability: Available
  • 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.

  • Editors

    Pieter Belmans, Université du Luxembourg
    Pieter Belmans is Assistant Professor of Mathematics at the University of Luxembourg. He studies algebraic geometry and noncommutative algebra from the point-of-view of derived categories. He developed the infrastructure that runs the Stacks project.

    Wei Ho, University of Michigan, Ann Arbor
    Wei Ho is Associate Professor of Mathematics at the University of Michigan. Her research interests are primarily in arithmetic geometry, number theory, and algebraic geometry. She first became involved with the Stacks project during her postdoc at Columbia University.

    Aise Johan de Jong, Columbia University, New York
    Aise Johan de Jong is Professor at Columbia University. He has worked at Harvard University, Princeton University, and MIT. Currently he spends most of his research time advising his graduate students and working on the Stacks project. He received the 2022 AMS Leroy P. Steele Prize for Mathematical Exposition for his work on the Stacks project.

    Contributors

    Raymond Cheng, Carl Lian, Takumi Murayama, Elsa Corniani, Neeraj Deshmukh, Brett Nasserden, Emanuel Reinecke, Nawaz Sultani, Rachel Webb, Jarod Alper, Pieter Belmans, Daniel Bragg, Jason Liang, Tuomas Tajakka, Haoyang Guo, Sanal Shivaprasad, Dylan Spence, Yueqiao Wu, Lena Ji, Matt Larson, Noah Olander, Shizhang Li, Patrick McFaddin, Drew Moore, Matthew Stevenson, Stephen McKean, Soumya Sankar, Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte, Kirsten Wickelgren, Yifei Zhao

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