DG-methods for microlocalization
| dc.creator | Guillermou, Stephane | |
| dc.date | 2008-11-25 | |
| dc.date.accessioned | 2026-07-07T10:36:32Z | |
| dc.date.available | 2026-07-07T10:36:32Z | |
| dc.description | For a complex manifold $X$ the ring of microdifferential operators $\E_X$ acts on the microlocalization $μhom(F,Ø_X)$, for $F$ in the derived category of sheaves on $X$. Kashiwara, Schapira, Ivorra, Waschkies proved, as a byproduct of their new microlocalization functor for ind-sheaves, $μ_X$, that $μhom(F,Ø_X)$ can in fact be defined as an object of the derived category of $\E_X$-modules: this follows from the fact that $μ_X Ø_X$ is concentrated in one degree. In this paper we prove that the tempered microlocalization also is an object of the derived category of $\E_X$-modules. Since we don't know whether the tempered version of $μ_X Ø_X$ is concentrated in one degree, we introduce a method to build suitable resolutions for which the action of $\E_X$ is realized in the category of complexes. We define a version of the de Rham algebra on the subanalytic site which is quasi-injective and we work in the category of dg-modules over this de Rham algebra instead of the derived category of sheaves. | |
| dc.identifier | https://arxiv.org/abs/0811.4080 | |
| dc.identifier | http://arxiv.org/abs/0811.4080 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/180084 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 35A27, 32C38 | |
| dc.title | DG-methods for microlocalization | |
| dc.type | text |