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Thursday 26 Feb 2015Drinfeld's p-adic symmetric regions and moduli of p-divisible groups

Thomas Zink - Bielefeld

H103 11:00-12:00

(joint work with M.Rapoport)

Let $K$ be a local field. Let $d \geq 2$. The rigid analytic space
$\Omega^d$ is $\mathbb{P}^{d-1}(\mathbb{C}_p)$ minus all hyperplanes
which are rational over $K$. Cerednik used $\Omega^{2}$ for the
$p$-adic uniformization of some Shimura curves. This is similar to the
uniformization of Riemann surfaces by the upper half plane. Drinfeld
interpreted $\Omega^{d}$ as a moduli problem of $p$-divisible groups
and deduced Cerednik's result from it.

We define new moduli problems and show that the lead also to
$\Omega^d$. According to Kudla and Rapoport this leads to new examples
of $p$-adic uniformization

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