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Let $X=\mathbb{A}^{n}$ be complex affine space, and let $T^{*}X$ be itscotangent bundle. For any exact Lagrangian $L\subset T^{*}X$, we define a newinvariant, A, living in $ \text{Div}_{\mathbb{Q}/\mathbb{Z}}(L)$. We call thisinvariant the monodromy divisor of $L$. We conjecture that the existence of afinite order character of $\pi_{1}(L$) whose monodromy is exactly A defines anobstruction to attaching a holonomic $\mathcal{D}_{X}$-module M associated to L- here, the association goes via positive characteristic and p-supports. In thecase where $\mathbb{H}_{dR}^{1}(L)=0$, we prove this conjecture, and then go onthe show that the set of such holonomic $\mathcal{D}_{X}$-modules forms atorsor over the group of finite order characters of $\pi_{1}$. This proves aversion of a conjecture of Kontsevich. As a consequence, we deduce that thegroup of Morita autoequivalences of the n-th Weyl algebra is isomorphic to thegroup of symplectomorphisms of $T^{*}\mathbb{A}^{n}$. This generalizes an oldtheorem of Dixmier (in the case n=1) and settles a conjecture of Belov-Kaneland Kontsevich in general.

The p-cycle of Holonomic D-modules and Quantization of Exact Algebraic Lagrangians