Integral Models of Toroidal Compactifications with Projective Cone Decompositions

We construct integral models of toroidal compactifications of PEL-type Shimura varieties with projective cone decompositions as normalizations of certain explicit blowups of the corresponding minimal compactifications, generalizing works of Tai’s, Chai’s, Faltings and Chai’s, and the author’s in zero or good reduction characteristics. We show that such integral models still enjoy many features of the good reduction theory, regardless of the levels and ramifications involved.