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.