Deformations of overconvergent isocrystals on the projective line

Abstract

Let k be a perfect field of positive characteristic and Z an effective Cartier divisor in the projective line over k with complement U. In this note, we establish some results about the formal deformation theory of overconvergent isocrystals on U with fixed “local monodromy” along Z. En route, we show that a Hochschild cochain complex governs deformations of a module over an arbitrary associative algebra. We also relate this Hochschild cochain complex to a de Rham complex in order to understand the deformation theory of a differential module over a differential ring.