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# Jerry Yu Fu : A density theorem towards p-adic monodromy

We investigate the $p$-adic monodromy of certain kinds of abelian varieties in $\mathcal{A}_{g}$ and prove a formal density theorem for the locus of deformations with big monodromy. Also, we prove that the small monodromy locus of the deformation space of a supersingular elliptic curve is $p$-adic nowhere dense. The approach is based on a congruence condition of $p$-divisible groups and transform of data between the Rapoport-Zink spaces and deformation spaces.

**Category**: Number Theory**Duration**: 01:14:51**Date**: November 2, 2022 at 3:10 PM-
**Tags:**seminar, Number Theory Seminar

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