Title: Perfectoid Spaces
Subjects: Topological fields, Number theory -- Discontinuous groups and automorphic forms -- Galois representations, Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Varieties over finite and local fields, Algebraic geometry -- Cycles and subschemes -- Transcendental methods, Hodge theory, Algebraic geometry -- (Co)homology theory -- $p$-adic cohomology, crystalline cohomology, Algebraic geometry -- (Co)homology theory -- de Rham cohomology, Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Local ground fields, Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rigid analytic geometry, Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Modular and Shimura varieties, Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heights, Algebraic geometry -- Algebraic groups -- Formal groups, $p$-divisible groups