Geodesic
Algèbres de distributions et 𝒟-modules arithmétiques
Huyghe, Christine1  ; Schmidt, Tobias2 
1 Université de Strasbourg, France
2 Université de Rennes I, France
Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 1-76

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Let p be a prime number, V a complete discrete valuation ring of unequal caracteristics (0,p), G a smooth affine algebraic group over 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 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.

Publié le :
DOI : 10.4171/RSMUP/139-1
Classification : 20, 13, 16
Mots-clés : Arithmetic $\mathcal D$-modules, $p$-adic distribution algebras

Huyghe, Christine 1 ; Schmidt, Tobias 2

1 Université de Strasbourg, France
2 Université de Rennes I, France 
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     title = {Alg\`ebres de distributions et $\mathcal D$-modules arithm\'etiques},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--76},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {139},
     year = {2018},
     doi = {10.4171/RSMUP/139-1},
     zbl = {1485.14034},
     mrnumber = {3825180},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/139-1/}
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Huyghe, Christine; Schmidt, Tobias. Algèbres de distributions et $\mathcal D$-modules arithmétiques. Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 1-76. doi: 10.4171/RSMUP/139-1

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