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- Title
Duality theorems for curves over local fields.
- Authors
Krishna, Amalendu; Rathore, Jitendra; Sadhukhan, Samiron
- Abstract
We prove duality theorems for the étale cohomology of split tori on smooth curves over a local field of positive characteristic. In particular, we show that the classical Brauer–Manin pairing between the Brauer and Picard groups of smooth projective curves over such a field extends to arbitrary smooth curves over the field. As another consequence, we obtain a description of the Brauer group of the function fields of curves over local fields in terms of the characters of the idele class groups.
- Subjects
BRAUER groups; PICARD groups; COHOMOLOGY theory
- Publication
Transactions of the American Mathematical Society, Series B, 2024, Vol 11, p945
- ISSN
2330-0000
- Publication type
Article
- DOI
10.1090/btran/187