Tate duality in positive dimension and applications
Abstract/Contents
- Abstract
- In Part I, we generalize classical Tate duality (local duality, nine-term exact sequence, etc.) for finite discrete Galois modules (i.e., finite etale commutative group schemes) over global fields to all affine commutative group schemes of finite type (the "positive-dimensional" case), building upon recent work of Cesnavicius generalizing Tate duality to all finite commutative group schemes (the "zero-dimensional" case). We concentrate mainly on the more difficult function field setting, giving some remarks about the easier number field case along the way. In Part II, we give applications of this extension of Tate duality to the study of Picard groups, Tate-Shafarevich sets, and Tamagawa numbers of linear algebraic groups over global function fields.
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 | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Rosengarten, Zev |
|---|---|
| Degree supervisor | Conrad, Brian, 1970- |
| Thesis advisor | Conrad, Brian, 1970- |
| Thesis advisor | Tsai, Cheng-Chiang |
| Thesis advisor | Vakil, Ravi |
| Degree committee member | Tsai, Cheng-Chiang |
| Degree committee member | Vakil, Ravi |
| Associated with | Stanford University, Department of Mathematics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Zev Rosengarten. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Zev Setchen Rosengarten
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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