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Delta waves have been described as periods of generalized silence across the cortex, and their alternation with periods of endogenous activity results in the slow oscillation of slow-wave sleep. Despite evidence that delta waves are instrumental for memory consolidation, their specific role in reshaping cortical functional circuits remains puzzling. In a rat model, we found that delta waves are not periods of complete silence and that the residual activity is not mere neuronal noise. Instead, cortical cells involved in learning a spatial memory task subsequently formed cell assemblies during delta waves in response to transient reactivation of hippocampal ensembles during ripples. This process occurred selectively during endogenous or induced memory consolidation. Thus, delta waves represent isolated cortical computations tightly related to ongoing information processing underlying memory consolidation.