Rings of microdifferential operators for arithmetic $\mathscr{D}$-modules

Details Rings of microdifferential operators for arithmetic $\mathscr{D}$-modules Rings of microdifferential operators for arithmetic $\mathscr{D}$-modules

2011-04-08

arxiv.org/abs/1104.1574v2

Mathematics

Algebraic Geometry

Scientific paper

The aim of this paper is to develop a theory of microdifferential operators for arithmetic $\mathscr{D}$-modules. We first define the sheaves of microdifferential operators of arbitrary levels on arbitrary smooth formal schemes. A difficulty lies in the fact that there are no homomorphisms between sheaves of microdifferential operators of different levels. To remedy this, we define the intermediate differential operators, and using these, we define the sheaf of microdifferential operators for $\mathscr{D}^\dag$. We conjecture that the characteristic variety of a $\mathscr{D}^\dag$-module is computed as the support of the microlocalization of a $\mathscr{D}^\dag$-module, and prove it in the curve case.

Affiliated with

Also associated with

No associations

Rating

Rings of microdifferential operators for arithmetic $\mathscr{D}$-modules 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 Rings of microdifferential operators for arithmetic $\mathscr{D}$-modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rings of microdifferential operators for arithmetic $\mathscr{D}$-modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-354930