Geodesic
Rings of microdifferential operators for arithmetic 𝒟-modules — Construction and an application to the characteristic varieties for curves
[Anneaux d'opérateurs microdifférentiels pour les 𝒟-modules arithmétiques. Construction et application aux variétés caractéristiques de courbes]
Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 1, pp. 35-107

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One aim of this paper is to develop a theory of microdifferential operators for arithmetic 𝒟-modules. We first define the rings of microdifferential operators of arbitrary levels on arbitrary smooth formal schemes. A difficulty lies in the fact that there is no homomorphism between rings of microdifferential operators of different levels. To remedy this, we define the intermediate differential operators, and using these, we define the ring of microdifferential operators for 𝒟†. We conjecture that the characteristic variety of a 𝒟†-module is computed as the support of the microlocalization of a 𝒟†-module, and prove it in the curve case.

Publié le :
DOI : 10.24033/bsmf.2680 
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     author = {Abe, Tomoyuki},
     title = {Rings of microdifferential operators for arithmetic $\mathcal {D}$-modules {\textemdash} {Construction} and an application to the characteristic varieties for curves},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {35--107},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
     number = {1},
     year = {2015},
     doi = {10.24033/bsmf.2680},
     mrnumber = {3323344},
     zbl = {1311.32003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2680/}
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Abe, Tomoyuki. Rings of microdifferential operators for arithmetic $\mathcal {D}$-modules — Construction and an application to the characteristic varieties for curves. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 1, pp. 35-107. doi: 10.24033/bsmf.2680

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