Perfectoid Shimura varieties of abelian type

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.

37 pages; slightly revised version, to appear in IMRN

References in corpus (2)

• Relative p-adic Hodge theory: Foundations
• On the p-adic cohomology of the Lubin-Tate tower