Deformations of overconvergent isocrystals on the projective line

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