For every Witt-vector level n, the local Hodge-Witt cohomology of Drinfeld's upper half space is generated over the new ring of Witt differential operators by a finitely generated submodule, extending the known n=1 theorem.
Differential Forms on General Commutative Algebras
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On Hodge--Witt cohomology of Drinfeld's upper half space over a finite field
For every Witt-vector level n, the local Hodge-Witt cohomology of Drinfeld's upper half space is generated over the new ring of Witt differential operators by a finitely generated submodule, extending the known n=1 theorem.