**Title:** D-modules mod p and microlocalization

**Speaker:** Thomas Bitoun

**Speaker Info:** MIT

**Brief Description:**

**Special Note**:

**Abstract:**

The talk is about reductions mod p of D-modules, viewed as a kind of microlocalization, that is localization on the cotangent bundle.The classical story goes that the algebra of differential operators D is filtered and that the associated graded algebra is commutative and naturally identified with functions on the cotangent bundle. Considering suitable filtrations of modules and their associated graded, one may define the singular support of a D-module, a Zariski closed subset of the cotangent bundle. A theorem of Gabber gives restrictions on the geometry of the singular supports, namely they should be involutive subsets of the cotangent bundle.

It turns out that a similar setting is provided by considering the center of the reduction mod p of the algebra of differential operators. We will present an analog of Gabber theorem in that setting. Some other key words are Azumaya algebra and p-curvature.

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