Kashiwara’s theorem for twisted arithmetic differential operators

We establish a version of Kashiwara’s theorem for twisted sheaves of Berthelot’s arithmetic differential operators for a closed immersion between smooth <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -adic formal schemes. As an application, we give a geometric construction of simple modules for crystalline distribution algebras of reductive groups.