Joint PU/IAS Number Theory

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