A filter for the filtration of a fluid, such as a liquid, comprising or composed of a support element made of a porous ceramic material, said element exhibiting a tubular or parallelepipedal shape delimited by an external surface and comprising, in its internal portion, a set of adjacent channels with axes parallel to one another and separated from one another by walls of said porous inorganic material, in which: - at least a portion of said channels are covered on their internal surface with a porous separating membrane layer and/or - at least a portion of said external surface is covered with a porous separating membrane layer; said filter being characterized in that: - said separating membrane layer is made of a material essentially composed of silicon carbide (SiC), - elemental nitrogen is present at the grain boundaries and in the SiC grains constituting the separating membrane layer, the content by weight of elemental nitrogen of the porous separating membrane layer, determined after melting under an inert gas, being between 0.1% and 2%, - the median pore diameter of the separating membrane layer, measured by analysis of photographs obtained by scanning electron microscopy, is between 10 nanometers and 5 micrometers, - the porosity of the separating membrane layer, measured by analysis of photographs obtained by scanning electron microscopy, is between 30 and 70%, - the median size of the SiC grains in said material, measured by analysis of photographs obtained by scanning electron microscopy, is between 20 nanometers and 10 micrometers. - at least a portion of said channels are covered on their internal surface with a porous separating membrane layer and/or - at least a portion of said external surface is covered with a porous separating membrane layer; said filter being characterized in that: - said separating membrane layer is made of a material essentially composed of silicon carbide (SiC), - elemental nitrogen is present at the grain boundaries and in the SiC grains constituting the separating membrane layer, the content by weight of elemental nitrogen of the porous separating membrane layer, determined after melting under an inert gas, being between 0.1% and 2%, - the median pore diameter of the separating membrane layer, measured by analysis of photographs obtained by scanning electron microscopy, is between 10 nanometers and 5 micrometers, - the porosity of the separating membrane layer, measured by analysis of photographs obtained by scanning electron microscopy, is between 30 and 70%, - the median size of the SiC grains in said material, measured by analysis of photographs obtained by scanning electron microscopy, is between 20 nanometers and 10 micrometers. - said separating membrane layer is made of a material essentially composed of silicon carbide (SiC), - elemental nitrogen is present at the grain boundaries and in the SiC grains constituting the separating membrane layer, the content by weight of elemental nitrogen of the porous separating membrane layer, determined after melting under an inert gas, being between 0.1% and 2%, - the median pore diameter of the separating membrane layer, measured by analysis of photographs obtained by scanning electron microscopy, is between 10 nanometers and 5 micrometers, - the porosity of the separating membrane layer, measured by analysis of photographs obtained by scanning electron microscopy, is between 30 and 70%, - the median size of the SiC grains in said material, measured by analysis of photographs obtained by scanning electron microscopy, is between 20 nanometers and 10 micrometers.