Algebraization theorems for coherent sheaves on stacks
Abstract/Contents
- Abstract
- Given a moduli problem, two important questions one can ask are the following: Is there an algebraic stack representing the moduli problem? If so, does it have a coarse space? A necessary step to answering these questions in the post-GIT era is to prove an algebraization result akin to formal GAGA for proper schemes. In this dissertation, we will present two such results. The first result (Chapter 2) is Grothendieck's existence theorem for relatively perfect complexes on an algebraic stack. This generalizes work of Lieblich in the setting of algebraic spaces. The second result (Chapter 3) is coherent completeness of BG (with G a split reductive group) and [\SL_d \backslash \mathbf{A}^d]. The results of this chapter are joint work with Jack Hall and are an important step to extending the \'{e}tale slice theorem of Alper-Hall-Rydh to positive characteristic. Finally, in future work with Jack Hall and Jarod Alper, we prove that an arbitrary [G \backslash \spec A] with G reductive is coherently complete
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2020; ©2020 |
| Publication date | 2020; 2020 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Lim, David Benjamin Weixuan |
|---|---|
| Degree supervisor | Alper, Jarod |
| Degree supervisor | Vakil, Ravi |
| Thesis advisor | Alper, Jarod |
| Thesis advisor | Vakil, Ravi |
| Thesis advisor | Taylor, Richard |
| Degree committee member | Taylor, Richard |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | David Benjamin Weixuan Lim |
|---|---|
| Note | Submitted to the Department of Mathematics |
| Thesis | Thesis Ph.D. Stanford University 2020 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by David Benjamin Weixuan Lim
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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