On a real analytic manifold M we have defined with Kashiwara in [KS01] the Grothendieck subanalytic topology, for which we only consider open subanalytic sets and finite coverings. This topology allows us in particular to define the sheaf of holomorphic functions with temperate growth on a complex manifold. Recently, with Guillermou [GS12] we have refined this topology and obtained the linear subanalytic topology, with same open sets but less coverings. This topology allows us to define sheaf of holomorphic functions with a given growth and thus a filtration on the sheaf of temperate holomorphic functions. Using Kashiwara's solution of the Riemann-Hilbert correspondence, we can then endow functorially regular holonomic D-modules with a filtration. We can also define sheaves with Gevrey growth which appear naturally in the study of irregular D-modules. References [GS12] S. Guillermou and P. Schapira Subanalytic topologies I. Construction of sheaves, arXiv:math.AG:1212.4326 [KS01] M. Kashiwara and P. Schapira, Ind-sheaves, Asterisque Soc. Math. France. 271 (2001).
Seminar on Analysis at University of Tsukuba