Microsupport of tempered solutions of D-Modules associated to smooth morphisms

Details Microsupport of tempered solutions of D-Modules associated to smooth morphisms Microsupport of tempered solutions of D-Modules associated to smooth morphisms

2008-08-06

arxiv.org/abs/0808.0887v3

Mathematics

Algebraic Geometry

27 pages, one section supressed to be published as a separate work (with D.Barlet), typos corrected, the main proofs are more

Scientific paper

Let $f:X\to Y$ be a smooth morphism of complex analytic manifolds and let $F$ be an $\mathbb{R}$-constructible complex on $Y$. Let $\cal{M}$ be a coherent $\shd_X$-module. We prove that the microsupport of the solution complex of $\shm$ in the tempered holomorphic functions $t \shh \text{om} (f^{-1} F, \sho_X)$, is contained in the 1-characteristic variety of $\cal{M}$ associated to $f$, and that the microsupport of the solution complex in the tempered microfunctions $t\mu hom(f^{-1}F, \sho_X)$ is contained in the 1-microcharacteristic variety of the microlocalized of $\shm$ along $T^*Y\times_Y X$. This applies in particular to the complex of solutions of $\shm$ in the sheaf of distributions holomorphic in the fibers of an arbitrary smooth morphism.

Affiliated with

Also associated with

No associations

Rating

Microsupport of tempered solutions of D-Modules associated to smooth morphisms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Microsupport of tempered solutions of D-Modules associated to smooth morphisms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Microsupport of tempered solutions of D-Modules associated to smooth morphisms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-28529