Perfectoid covers of abelian varieties

Abstract

For an abelian variety $A$ over an algebraically closed non-archimedean field of residue characteristic $p$, we show that there exists a perfectoid space which is the tilde-limit of ${\underleftarrow{\lim }}_{[p]}A$. Our proof also works for the larger class of abeloid varieties.

References in corpus (2)

• Relative p-adic Hodge theory, II: Imperfect period rings
• The cohomology of the moduli space of curves at infinite level

Cited by in corpus (5)

• The $p$-adic Corlette-Simpson correspondence for abeloids
• Pro-étale uniformisation of abelian varieties
• Cusps and $q$-expansion principles for modular curves at infinite level
• The cohomology of the moduli space of curves at infinite level
• On Picard Groups of Perfectoid Covers of Toric Varieties