  Inflation near a maximum of the potential is studied when non-local
derivative operators are included in the inflaton Lagrangian. Such terms can
impose additional sources of friction on the field. For an arbitrary spacetime
geometry, these effects can be quantified in terms of a local field theory with
a potential whose curvature around the turning point is strongly suppressed.
This implies that a prolonged phase of slow-roll inflation can be achieved with
potentials that are otherwise too steep to drive quasi-exponential expansion.
We illustrate this mechanism within the context of p-adic string theory.
