Filtered restriction of geometric D-modules

Rémi Arcadias (1)

1 Universidad de Sevilla = University of Seville

In D-module theory, we have the notion of the restriction of a module along a smooth variety. T. Oaku and N. Takayama have described a process to compute the restriction, which starts from a free resolution adapted to the V-filtration of Kashiwara-Malgrange. By using the theory of free resolutions adapted to the (order and V)-bifiltration (from T. Oaku , N. Takayama and M. Granger), we endow the restriction with an order filtration and we show that the process of Oaku and Takayama respects the order filtration. In consequence, we compute a minimal presentation of the algebraic local cohomology module associated with a quasi-homogeneous polynomial with an isolated singularity, viewed as a D-module and endowed with a kind of a pole order filtration.

Mots clés: D-module; restriction; free resolution; algebraic local cohomology

Domaines: Géométrie algébrique [math.AG]

Rémi Arcadias. Filtered restriction of geometric D-modules. 2012. ⟨hal-00661640⟩