Perfectoid Shimura varieties of abelian type

TL;DR

This paper proves that certain complex algebraic varieties called Shimura varieties of abelian type, along with related moduli spaces of K3 surfaces, are perfectoid when considered at infinite level at a prime p.

Contribution

It establishes the perfectoid property for Shimura varieties of abelian type and related K3 surface moduli spaces at infinite p-level, extending the scope of perfectoid geometry.

Findings

Shimura varieties of abelian type are perfectoid at infinite p-level

Moduli spaces of polarized K3 surfaces are perfectoid at infinite p-level

Provides new tools for p-adic geometry and arithmetic applications

Abstract

We prove that Shimura varieties of abelian type with infinite level at $p$ are perfectoid. As a corollary, the moduli spaces of polarized K3 surfaces with infinite level at $p$ are also perfectoid.