Mathematical Research Letters

Volume 21 (2014)

Number 5

On the moduli space of deformations of a $p$-divisible group

Pages: 1015 – 1045



Oleg Demchenko (Department of Mathematics and Mechanics, St. Petersburg State University, St.Petersburg, Russia)

Alexander Gurevich (Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel)


Let $G$ be a connected $p$-divisible group of height $h$ and dimension $d$ over a perfect field $k$, and $\mathcal{O}$ denote the ring of Witt vectors over $k$. It is a well-known fact that the deformation functor $\mathcal{D}ef_G$ is representable by $\mathrm{Spf}_{\mathcal{O}}\mathcal{O}[[t_1, \dots , t_{d(h-d)}]]$. Following Hazewinkel’s philosophy we construct explicitly a family of universal deformations of $G$.

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