Smooth Compactifications of Locally Symmetric Varieties: Frontmatter

By A. Ash, D. Mumford, Michael Rapoport, Yung-sheng Tai. 2010

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Arithmetic Compactifications of PEL-Type Shimura Varieties (2013, background): “Although all results to be stated have their analytic analogues over the complex numbers, the analytic techniques in [17] and [16] do not carry over naively.”
Toroidal compactifications of integral models of Shimura varieties of Hodge type (2012, background): “[AMRT10]) constructed good, toroidal compactifications in the general setting of arithmetic quotients of hermitian symmetric domains.”
Finsler bordifications of symmetric and certain locally symmetric spaces (2015, background): “Let us mention the work of Satake [48], who was the first to define Satake compactifications of symmetric spaces of noncompact type and used it in [47] to construct compactifications of certain arithmetic locally symmetric spaces, Furstenberg [19], who constructed compactifications of symmetric spac”
A note on the cone conjecture for K3 surfaces in positive characteristic (2011, background): “This is one of the homogeneous selfadjoint convex cones in the sense of [2].”
Moduli of K3 Surfaces and Irreducible Symplectic Manifolds (2010, methodology): “Denoting the map x ∈ D(F ) 7→ Im(prU (x)) ∈ U(F ) by φF , as in [AMRT], we have the diagram”