We prove a precise bound on the number of sections of a pure sheaf on a projective scheme. Our result strengthens the Le Potier-Simpson estimate and generalizes it to schemes defined over a field of any characteristic. This is used to construct the moduli space of semistable sheaves in mixed characteristic via Simpson's method.
Adrian Langer. "Moduli spaces of sheaves in mixed characteristic." Duke Math. J. 124 (3) 571 - 586, 15 September 2004. https://doi.org/10.1215/S0012-7094-04-12434-0