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Local cohomology and \(\mathcal D\)-affinity in positive characteristic. (English) Zbl 1016.14009

Summary: We give an example of a \(\mathcal D\)-module on a Grassmann variety in positive characteristic with non-vanishing first cohomology group. This is a counterexample to \(\mathcal D\)-affinity and the Beilinson-Bernstein equivalence for flag manifolds in positive characteristic.

MSC:

14F17 Vanishing theorems in algebraic geometry
14G15 Finite ground fields in algebraic geometry
13D45 Local cohomology and commutative rings
14M15 Grassmannians, Schubert varieties, flag manifolds
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References:

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