Soit le corps des nombres -adiques et un schéma en groupes réductif, connexe et déployé sur . Nous introduirons un faisceau d’opérateurs différentiels arithmétiques tordus sur la variété des drapeaux formelle de , associée à un caractère général. En particulier, nous généraliserons les résultats de [21], concernant la -affinité de la variété des drapeaux formelle lisse de , de certains gerbes d’opérateurs différentiels arithmétiques tordus -adiquement complets, associés à un caractère algébrique, et les résultats de [24] concernant le calcul des sections globales.
Let be the field of -adic numbers and a split connected reductive group scheme over . In this work we will introduce a sheaf of twisted arithmetic differential operators on the formal flag variety of , associated to a general character. In particular, we will generalize the results of [21], concerning the -affinity of the smooth formal flag variety of , of certain sheaves of -adically complete twisted arithmetic differential operators associated to an algebraic character, and the results of [24] concerning the calculation of the global sections.
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Mots clés : Formal flag variety, twisted arithmetic differential operators, Beilinson–Bernstein correspondence
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@article{JTNB_2024__36_1_1_0, author = {Andr\'es Sarrazola-Alzate}, title = {A {Beilinson{\textendash}Bernstein} {Theorem} for {Twisted} {Arithmetic} {Differential} {Operators} on the {Formal} {Flag} {Variety}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {1--43}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {36}, number = {1}, year = {2024}, doi = {10.5802/jtnb.1272}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1272/} }
TY - JOUR AU - Andrés Sarrazola-Alzate TI - A Beilinson–Bernstein Theorem for Twisted Arithmetic Differential Operators on the Formal Flag Variety JO - Journal de théorie des nombres de Bordeaux PY - 2024 SP - 1 EP - 43 VL - 36 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1272/ DO - 10.5802/jtnb.1272 LA - en ID - JTNB_2024__36_1_1_0 ER -
%0 Journal Article %A Andrés Sarrazola-Alzate %T A Beilinson–Bernstein Theorem for Twisted Arithmetic Differential Operators on the Formal Flag Variety %J Journal de théorie des nombres de Bordeaux %D 2024 %P 1-43 %V 36 %N 1 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1272/ %R 10.5802/jtnb.1272 %G en %F JTNB_2024__36_1_1_0
Andrés Sarrazola-Alzate. A Beilinson–Bernstein Theorem for Twisted Arithmetic Differential Operators on the Formal Flag Variety. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 1, pp. 1-43. doi : 10.5802/jtnb.1272. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1272/
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