Uniform sheaves and differential equations

Abstract

Real blow-ups and more refined "zooms" play a key role in the analysis of singularities of complex-analytic differential modules. They do not change the underlying topology, but the uniform structure. This suggests to revisit the cohomology theory of differential modules with help of a suitable new notion of uniform sheaves based on the uniformity rather than the topology. We also investigate the $p$-adic situation (in particular, an analog of real blow-ups) from this uniform viewpoint.