Number Theory
On period spaces for p-divisible groups
Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1123-1128.

In their book Rapoport and Zink constructed rigid analytic period spaces for Fontaine's filtered isocrystals, and period morphisms from moduli spaces of p-divisible groups to some of these period spaces. We determine the image of these period morphisms, thereby contributing to a question of Grothendieck. We give examples showing that only in rare cases the image is all of the Rapoport–Zink period space.

Dans leur livre, Rapoport et Zink ont construit des espaces de périodes, rigides analytiques pour les isocristaux filtrés de Fontaine. Ils ont construits également des morphismes de périodes entre des espaces modulaires des groupes de Barsotti–Tate et certains de leurs espaces de périodes. Dans cette Note nous déterminons l'image des morphismes de périodes, contribuant ainsi à une question de Grothendieck. Nous donnons des examples montrant que l'image ne coïncide que rarement avec tout l'espace de périodes de Rapoport–Zink.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.07.003
Hartl, Urs 1

1 University of Münster, Institute of Mathematics, Einsteinstr. 62, 48149 Münster, Germany
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Hartl, Urs. On period spaces for p-divisible groups. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1123-1128. doi : 10.1016/j.crma.2008.07.003. http://www.numdam.org/articles/10.1016/j.crma.2008.07.003/

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