Distribution algebras and arithmetic \(\mathcal{D}\)-modules
Summary: Let \(p\) be a prime number, \(V\) a complete discrete valuation ring of unequal caracteristics \((0,p)\), \(G\) a smooth affine algebraic group over \(\operatorname{Spec} V\). Using partial divided powers techniques of Berthelot, we construct arithmetic distribution algebras, with level \(m\), generalizing the classical construction of the distribution algebra. We also construct the weak completion of the classical distribution algebra over a finite extension \(K\) of \(\mathbb{Q}_p\). We then show that these distribution algebras can be identified with invariant arithmetic differential operators over \(G\), and prove a coherence result when the ramification index of \(K\) is \(<p-1\).
scientific article; zbMATH DE number 6898039