Rendiconti del Seminario Matematico della Università di Padova

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Volume 128, 2012, pp. 345–372
DOI: 10.4171/RSMUP/128-9

Published online: 2012-12-31

Uniform Sheaves and Differential Equations

Yves André[1]

(1) Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), France

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, the analog of real blow-ups) from this uniform viewpoint.

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André Yves: Uniform Sheaves and Differential Equations. Rend. Sem. Mat. Univ. Padova 128 (2012), 345-372. doi: 10.4171/RSMUP/128-9