A nonvolatile memory cell, memory cell arrangement, and method for production of a nonvolatile memory cell is disclosed. The nonvolatile memory cell includes a vertical field-effect transistor (FET). The FET contains a nanoelement arranged as a channel region and an electrically insulating layer. The electrically insulating layer at least partially surrounds the nanoelement and acts as a charge storage layer and as a gate-insulating layer. The electrically insulating layer is arranged such that electrical charge carriers may be selectively introduced into or removed from the electrically insulating layer and the electrical conductivity characteristics of the nanoelement may be influenced by the electrical charge carriers introduced into the electrically insulating layer.