Étale Steenrod operations and the Artin-Tate pairing
Abstract/Contents
- Abstract
- We prove a 1966 conjecture of Tate concerning the Artin-Tate pairing on the Brauer group of a surface over a finite field, which is the analogue of the Cassels-Tate pairing. Tate asked if this pairing is always alternating and we find an affirmative answer, which is somewhat surprising in view of the work of Poonen-Stoll on the Cassels-Tate pairing. Our method is based on studying a connection between the Artin-Tate pairing and (generalizations of) Steenrod operations in etale cohomology. Inspired by an analogy to the algebraic topology of manifolds, we develop tools allowing us to calculate the relevant etale Steenrod operations in terms of characteristic classes.
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 | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Feng, Tony |
|---|---|
| Degree supervisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Taylor, R. L. (Richard Lawrence), 1962- |
| Thesis advisor | Vakil, Ravi |
| Degree committee member | Taylor, R. L. (Richard Lawrence), 1962- |
| Degree committee member | Vakil, Ravi |
| Associated with | Stanford University, Department of Mathematics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Tony Feng. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by Tony Feng
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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