Method for calcining mineral rock in a parallel-flow regenerative vertical shaft kiln, wherein at least two shafts are interconnected by a gas transfer channel, this method comprising, in production mode, - loading carbonate mineral rock at the top of the kiln, - preheating this rock, - firing this rock with its decarbonation into calcined material, - cooling the calcined material by cooling air, and - unloading the calcined material at the bottom of the shafts, - each shaft operating alternately in firing mode and in preheating mode, one shaft being in firing mode for a predetermined period of time while at least one other shaft is in preheating mode, and vice versa, - the firing mode comprising: said loading of carbonate mineral rock at the top of the shaft in firing mode, in the presence of said preheated carbonate mineral rock, during descending into this shaft, a combustion of fuel in the presence of oxygen so as to obtain said firing of this rock and its decarbonation into calcined material with the release of combustion fumes in the form of a gaseous current descending in a co-current manner in the shaft in firing mode, and passage of said gaseous current containing these combustion fumes from the shaft in firing mode to said at least one shaft in preheating mode via said gas transfer channel, - the preheating mode comprising: said preheating of the loaded carbonate mineral rock by heat exchange with the gas stream containing the combustion fumes, coming from the gas transfer channel, which is ascending in said at least one shaft in preheating mode, in a counter-current manner of said loaded carbonate mineral rock, and discharging from the kiln of a gaseous effluent originating from the gas stream containing the combustion fumes, at the top of said at least one shaft in preheating mode, characterised in that it further comprises - collecting a part of the gaseous effluent discharged from the kiln, - formation of an oxidising mixture by mixing said part collected from the gaseous effluent discharged from the kiln with concentrated dioxygen, and - an introduction of this oxidising mixture at the top of the shaft in firing mode so as to ensure said combustion of fuel in the presence of oxygen, the gaseous effluent discharged from the kiln being concentrated in CO 2 and having a CO 2 content of at least 60%, in particular at least 80%, and particularly advantageously at least 90% by volume for dry gas. - loading carbonate mineral rock at the top of the kiln, - preheating this rock, - firing this rock with its decarbonation into calcined material, - cooling the calcined material by cooling air, and - unloading the calcined material at the bottom of the shafts, - each shaft operating alternately in firing mode and in preheating mode, one shaft being in firing mode for a predetermined period of time while at least one other shaft is in preheating mode, and vice versa, - the firing mode comprising: said loading of carbonate mineral rock at the top of the shaft in firing mode, in the presence of said preheated carbonate mineral rock, during descending into this shaft, a combustion of fuel in the presence of oxygen so as to obtain said firing of this rock and its decarbonation into calcined material with the release of combustion fumes in the form of a gaseous current descending in a co-current manner in the shaft in firing mode, and passage of said gaseous current containing these combustion fumes from the shaft in firing mode to said at least one shaft in preheating mode via said gas transfer channel, said loading of carbonate mineral rock at the top of the shaft in firing mode, in the presence of said preheated carbonate mineral rock, during descending into this shaft, a combustion of fuel in the presence of oxygen so as to obtain said firing of this rock and its decarbonation into calcined material with the release of combustion fumes in the form of a gaseous current descending in a co-current manner in the shaft in firing mode, and passage of said gaseous current containing these combustion fumes from the shaft in firing mode to said at least one shaft in preheating mode via said gas transfer channel, - the preheating mode comprising: said preheating of the loaded carbonate mineral rock by heat exchange with the gas stream containing the combustion fumes, coming from the gas transfer channel, which is ascending in said at least one shaft in preheating mode, in a counter-current manner of said loaded carbonate mineral rock, and discharging from the kiln of a gaseous effluent originating from the gas stream containing the combustion fumes, at the top of said at least one shaft in preheating mode, characterised in that it further comprises said preheating of the loaded carbonate mineral rock by heat exchange with the gas stream containing the combustion fumes, coming from the gas transfer channel, which is ascending in said at least one shaft in preheating mode, in a counter-current manner of said loaded carbonate mineral rock, and discharging from the kiln of a gaseous effluent originating from the gas stream containing the combustion fumes, at the top of said at least one shaft in preheating mode, characterised in that it further comprises - collecting a part of the gaseous effluent discharged from the kiln, - formation of an oxidising mixture by mixing said part collected from the gaseous effluent discharged from the kiln with concentrated dioxygen, and - an introduction of this oxidising mixture at the top of the shaft in firing mode so as to ensure said combustion of fuel in the presence of oxygen,