Brain activity generates extracellular voltage fluctuations recorded as local field potentials (LFPs). While known that the relevant micro-variables, the ionic currents across membranes, jointly generate the macro-variables, the extracellular voltage, neither the detailed biophysical knowledge nor the required computational power has been available to model these processes. We simulated the LFP in a model of the rodent neocortical column composed of >12,000 reconstructed, multi-compartmental and spiking cortical layer 4 and 5 pyramidal neurons and basket cells, including five million dendritic and somatic compartments with voltage- and ion-dependent currents, realistic connectivity and probabilistic AMPA, NMDA and GABA synapses. We found that, depending on a number of factors, the LFP reflects local and cross-layer processing and active currents dominate the generation of LFPs rather than synaptic ones. Spike-related currents impact the LFP not only at higher frequencies but lower than 50 Hz. This work calls for re-evaluating the genesis of LFPs.