Lectures on p-adic Differential Equations

The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. Contents 1 Introduction . . . . . . . Transcendental Theory . Hasse Invariants . The a --+ a' Map .