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On non-basic Rapoport-Zink spaces

Elena Mantovan (2008)

Annales scientifiques de l'École Normale Supérieure

In this paper we study certain moduli spaces of Barsotti-Tate groups constructed by Rapoport and Zink as local analogues of Shimura varieties. More precisely, given an isogeny class of Barsotti-Tate groups with unramified additional structures, we investigate how the associated (non-basic) moduli spaces compare to the (basic) moduli spaces associated with its isoclinic constituents. This aspect of the geometry of the Rapoport-Zink spaces is closely related to Kottwitz’s prediction that their l -adic...

On non-commutative twisting in étale and motivic cohomology

Jens Hornbostel, Guido Kings (2006)

Annales de l’institut Fourier

This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups H 1 ( 𝒪 K [ 1 / S ] , H i ( X ¯ , p ( j ) ) ) , where X Spec 𝒪 K [ 1 / S ] is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to H i ( X ¯ , p ( j ) ) . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.

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