Algèbres de distributions et -modules arithmétiques
Christine Huyghe
Université de Strasbourg, FranceTobias Schmidt
Université de Rennes I, France
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Abstract
Let be a prime number, a complete discrete valuation ring of unequal caracteristics , a smooth affine algebraic group over Spec . Using partial divided powers techniques of Berthelot, we construct arithmetic distribution algebras, with level , generalizing the classical construction of the distribution algebra. We also construct the weak completion of the classical distribution algebra over a finite extension of . We then show that these distribution algebras can be identified with invariant arithmetic differential operators over , and prove a coherence result when the ramification index of is .
Cite this article
Christine Huyghe, Tobias Schmidt, Algèbres de distributions et -modules arithmétiques. Rend. Sem. Mat. Univ. Padova 139 (2018), pp. 1–76
DOI 10.4171/RSMUP/139-1