Morphisms and cohomological comparison for Henselian schemes
Abstract/Contents
- Abstract
- The global analogue of a Henselian local ring is a Henselian pair - i.e., a ring R and an ideal I which satisfy a condition resembling Hensel's lemma regarding lifting coprime factorizations of polynomials over R/I to factorizations over R. The geometric counterpart is the notion of Henselian schemes, which can serve as an "algebraic" substitute for formal schemes in applications such as deformation theory. In this thesis we discuss Henselian schemes and quasi-coherence in detail, including the correction of an error in the existing literature concerning quasi-coherent sheaves on affine Henselian schemes. We also develop the theory of smooth and etale morphisms of Henselian schemes and prove that quasi-coherent sheaves on Henselian schemes are sheaves for the Henselian-etale topology. Finally, we prove a GAGA-style cohomology comparison result for Henselian schemes in in positive characteristic, and discuss algebraizability of coherent sheaves on the Henselization of a proper scheme.
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 | Devadas, Sheela | |
|---|---|---|
| Degree supervisor | Conrad, Brian, 1970- | |
| Thesis advisor | Conrad, Brian, 1970- | |
| Thesis advisor | Bump, Daniel, 1952- | |
| Thesis advisor | Vakil, Ravi | |
| Degree committee member | Bump, Daniel, 1952- | |
| Degree committee member | Vakil, Ravi | |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Sheela Devadas. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2020. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Sheela Devadas
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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