In this work, we investigate the implications of the Integrated Galaxy-wide stellar Initial Mass Function (IGIMF) approach in the framework of the semi-analytic model GAEA (GAlaxy Evolution and Assembly), which features a detailed treatment of chemical enrichment and stellar feedback. The IGIMF provides an analytic description of the dependence of the stellar IMF shape on the rate of star formation in galaxies. We find that our model with a universal IMF predicts a rather flat [$alpha$/Fe]-stellar mass relation. The model assuming the IGIMF, instead, is able to reproduce the observed increase of $alpha$-enhancement with stellar mass, in agreement with previous studies. This is mainly due to the fact that massive galaxies are characterized by larger star formation rates at high-redshift, leading to stronger $alpha$-enhancement with respect to low-mass galaxies. At the same time, the IGIMF hypothesis does not affect significantly the trend for shorter star formation timescales for more massive galaxies. We argue that in the IGIMF scenario the [$alpha$/Fe] ratios are good tracers of the highest star formation events. The final stellar masses and mass-to-light-ratio of our model massive galaxies are larger than those estimated from the synthetic photometry assuming a universal IMF, providing a self-consistent interpretation of similar recent results, based on dynamical analysis of local early type galaxies.
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