Claus Scheiderer, Joost van Hamel: Cohomology of tori over p-adic curves,

Submission: 2002, Jan 24

We establish a duality in the cohomology of arbitrary tori over smooth but not necessarily projective curves over a p-adic field. This generalises Lichtenbaum-Tate duality between the Picard group and the Brauer group of a smooth projective curve.

2000 Mathematics Subject Classification: Primary 14G20; secondary 14F22, 14L15, 11S25

Keywords and Phrases: lgebraic tori, etale cohomology, algebraic curves, p-adic fields, duality theorems, Lichtenbaum-Tate duality, Poincare duality, Brauer group, Picard group

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