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2-Cohomology of semi-simple simply connected group-schemes over curves defined over p -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

Let X be a proper, smooth, geometrically connected curve over a p -adic field k . Lichtenbaum proved that there exists a perfect duality: Br ( X ) × Pic ( X ) / between the Brauer and the Picard group of X , from which he deduced the existence of an injection of Br ( X ) in P X Br ( k P ) where P X and k P denotes the residual field of the point P . The aim of this paper is to prove that if G = G ˜ is an X e t - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results the neutrality of every X e t -gerb which...

[unknown]

Andrew R. Linshaw, Gerald W. Schwarz, Bailin Song (0)

Annales de l’institut Fourier

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