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.

59 pages; fixed typos, improved exposition; comments welcome!

References in corpus (4)

• Deformation theory via differential graded Lie algebras
• Local Fourier transforms and rigidity for D-modules
• Sur l'holonomie de D-modules arithmétiques associés à des F-isocristaux surconvergents sur des courbes lisses
• Deformations of overconvergent isocrystals on the projective line

Cited by in corpus (2)

• Etale and crystalline companions, I
• Deformations of overconvergent isocrystals on the projective line