We present a deep [OII] emission line survey of faint galaxies (22.5<KAB<24) in the Chandra Deep Field South and the FIRES field. With these data we measure the star formation rate (SFR) in galaxies in the stellar mass range 8.85 < log(M*/Msun) < 9.5 at 0.62<z<0.885, to a limit of SFR = 0.1Msun/yr. The presence of a massive cluster (MS1054-03) in the FIRES field, and of significant large scale structure in the CDFS field, allows us to study the environmental dependence of SFRs amongst this population of low-mass galaxies. Comparing our results with more massive galaxies at this epoch, with our previous survey (ROLES) at the higher redshift z=1, and with SDSS Stripe 82 data, we find no significant evolution of the stellar mass function of star-forming galaxies between z=0 and z=1, and no evidence that its shape depends on environment. The correlation between specific star formation rate (sSFR) and stellar mass at z=0.75 has a power-law slope of beta=-0.2, with evidence for a steeper relation at the lowest masses. The normalization of this correlation lies as expected between that corresponding to z=1 and the present day. The global SFR density is consistent with an evolution of the form (1+z)^2 over 0<z<1, with no evidence for a dependence on stellar mass. The sSFR of these star-forming galaxies at z=0.75 does not depend upon the density of their local environment. Considering just high-density environments, the low-mass end of the sSFR-M* relation in our data is steeper than that in Stripe 82 at z=0, and shallower than that measured by ROLES at z=1. Evolution of low-mass galaxies in dense environments appears to be more rapid than in the general field.
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