Algèbres de distributions et -modules arithmétiques
Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 1-76.
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 .
Publié le :
DOI : 10.4171/RSMUP/139-1
DOI : 10.4171/RSMUP/139-1
Classification :
20, 13, 16
Mots-clés : Arithmetic $\mathcal D$-modules, $p$-adic distribution algebras
Mots-clés : Arithmetic $\mathcal D$-modules, $p$-adic distribution algebras
Affiliations des auteurs :
Huyghe, Christine 1 ;
Schmidt, Tobias 2
@article{RSMUP_2018__139__1_0,
author = {Huyghe, Christine and Schmidt, Tobias},
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://www.numdam.org/articles/10.4171/RSMUP/139-1/}
}
TY - JOUR AU - Huyghe, Christine AU - Schmidt, Tobias TI - Algèbres de distributions et $\mathcal D$-modules arithmétiques JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2018 SP - 1 EP - 76 VL - 139 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/139-1/ DO - 10.4171/RSMUP/139-1 ID - RSMUP_2018__139__1_0 ER -
%0 Journal Article %A Huyghe, Christine %A Schmidt, Tobias %T Algèbres de distributions et $\mathcal D$-modules arithmétiques %J Rendiconti del Seminario Matematico della Università di Padova %D 2018 %P 1-76 %V 139 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/139-1/ %R 10.4171/RSMUP/139-1 %F RSMUP_2018__139__1_0
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. http://www.numdam.org/articles/10.4171/RSMUP/139-1/
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