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Let be a proper, smooth, geometrically connected curve over a -adic field . Lichtenbaum proved that there exists a perfect duality:between the Brauer and the Picard group of , from which he deduced the existence of an injection of in where and denotes the residual field of the point . The aim of this paper is to prove that if is an - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results the neutrality of every -gerb which...
We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are
indexed by the classes in a Weyl group modulo a subgroup, and each class has a
distinguished representative of minimal length. The main result of this paper is that the
dimension of a stratum equals the length of the corresponding Weyl group element. We also
discuss some explicit examples.
We show that the Zink equivalence between -divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic is compatible with duality. The proof relies on a new explicit formula for the -divisible group associated to a Dieudonné display.
A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ()-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ()-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the...
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