Overcoherence implies holonomicity

الأصل · EN

Let be a mixed characteristic complete discrete valuation ring with perfect residue field. Let be a smooth formal scheme over. We prove than a †, -module which is overcoherent after any change of basis is an holonomic †, -module. Furthermore, we check that this implies than a bounded complex of †,-modules is overholonomic after any change of basis if and only if, for any integer j, H ʲ () is overholonomic after any change of basis.