Étale Steenrod operations and the Artin-Tate pairing

Placeholder Show Content


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.


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


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.


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

© 2019 by Tony Feng
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

Also listed in

Loading usage metrics...