The integral Hodge polygon for p-divisible groups with endomorphism structure

Let p be a prime number, let O F be the ring of integers of a finite field extension F of Q p and let O K be a complete valuation ring of rank 1 and mixed characteristic (0, p).We introduce and study the integral Hodge polygon, a new invariant of p-divisible groups H over O K endowed with an action ι of O F .If F |Q p is unramified, this invariant recovers the classical Hodge polygon and only depends on the reduction of (H, ι) to the residue field of O K .This is not the case in general, whence the attribute "integral".The new polygon lies between Fargues' Harder-Narasimhan polygons of the p-power torsion parts of H and another combinatorial invariant of (H, ι) called the Pappas-Rapoport polygon.Furthermore, the integral Hodge polygon behaves continuously in families over a p-adic analytic space.5 The integral Hodge polygon in families 28 5.1 Continuity of the integral Hodge polygon . . . . . . . .