LERMA UMR8112

The origin of the stellar initial mass function (IMF) is one of the most debated
issues in astrophysics. I will discuss new insights into this problem based on a systematic census of prestellar cores and molecular filaments in nearby clouds taken as part of the Herschel Gould Belt survey, as well as higher-resolution observations with APEX/ArTéMiS and ALMA. Our results point to the key role of the quasi-universal filamentary structure pervading molecular clouds. They suggest that the dense cores making up the peak of the prestellar core mass function (CMF) - and indirectly the peak of the IMF - result from gravitational fragmentation of molecular filaments near the critical mass per unit length. The Salpeter power-law tail of the CMF/IMF may be at least partly inherited from the filament line mass function (FLMF), which is observed to follow a Salpeter-like power law in the regime of thermally supercritical filaments.