2011/04/08 by Tomoyuki Abe, Abe, Tomoyuki
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1104.1574
openalex publication_date 2011/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The aim of this paper is to develop a theory of microdifferential operators for arithmetic \mathscrD-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 \mathscrD^†. We conjecture that the characteristic variety of a \mathscrD^†-module is computed as the support of the microlocalization of a \mathscrD^†-module, and prove it in the curve case.