Cohomological rigidity via deformation theory

Shishir Agrawal

Published 2017-10-10Version 1

We formalize the intuition that cohomologically rigid overconvergent isocrystals on dense affine open subsets of the projective line over a perfect field of positive characteristic are the ones with no nontrivial infinitesimal deformations that preserve the Robba fibers. En route, we describe a general result showing that the Hochschild cochain complex governs deformations of modules over arbitrary associative algebras in characteristic 0, and we explain a relationship between the Hochschild cochain complex and the de Rham complex.