Abstract

I will first review what we know about the toroidal and minimal compactifications of Shimuravarieties and their integral models, and the well-positioned subschemes of these integral modelsThen l will explain some p-adic analogues of Harris and Zucker's work on the boundarycohomology of Shimura varieties and of well-positioned subschemes of their integral models (whendefined). (Based on thesis works of Peihang Wu and Shengkai Mao, and on joint work with DavidSherman on p-adic log Riemann-Hilbert functors in the ideally log smooth case.)