Étale Steenrod operations and the Artin–Tate pairing. (13th July 2020)
- Record Type:
- Journal Article
- Title:
- Étale Steenrod operations and the Artin–Tate pairing. (13th July 2020)
- Main Title:
- Étale Steenrod operations and the Artin–Tate pairing
- Authors:
- Feng, Tony
- Abstract:
- 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 analog 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 étale cohomology. Inspired by an analogy to the algebraic topology of manifolds, we develop tools allowing us to calculate the relevant étale Steenrod operations in terms of characteristic classes.
- Is Part Of:
- Compositio mathematica. Volume 156:Number 7(2020)
- Journal:
- Compositio mathematica
- Issue:
- Volume 156:Number 7(2020)
- Issue Display:
- Volume 156, Issue 7 (2020)
- Year:
- 2020
- Volume:
- 156
- Issue:
- 7
- Issue Sort Value:
- 2020-0156-0007-0000
- Page Start:
- 1476
- Page End:
- 1515
- Publication Date:
- 2020-07-13
- Subjects:
- 11G25
arithmetic geometry, -- Brauer groups, -- Steenrod operations, -- Artin–Tate conjecture
Mathematics -- Periodicals
510 - Journal URLs:
- http://journals.cambridge.org/action/displayJournal?jid=COM ↗
- DOI:
- 10.1112/S0010437X20007216 ↗
- Languages:
- English
- ISSNs:
- 0010-437X
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 3366.000000
British Library STI - ELD Digital Store - Ingest File:
- 15306.xml