\(\mathcal{D}\)-arithmetic modules on the flag variety. (\(\mathcal{D}\)-modules arithmétiques sur la variété de drapeaux.) (French. English summary) Zbl 1440.14100
Summary: Let \(p\) be a prime number, \(V\) a complete discrete valuation ring of unequal characteristics \((0,p)\), and \(G\) a connected split reductive algebraic group over \(\operatorname{Spec}V\). We obtain a localization theorem, involving arithmetic distributions, for the sheaf of arithmetic differential operators on the formal flag variety of \(G\). We give an application to the rigid cohomology of open subsets in the characteristic \(p\) flag variety.
MSC:
| 14F10 | Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 14G22 | Rigid analytic geometry |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
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