Revisiting FRB 20121102A: milliarcsecond localisation and a decreasing dispersion measure

FRB 20121102A is the original repeating fast radio burst (FRB) source and also the first to be localised to milliarcsecond precision using very-long-baseline interferometry (VLBI). It has been active for over 13 years and resides in an extreme magneto-ionic environment in a dwarf host galaxy at a distance of ~1 Gpc. In this work, we use the European VLBI Network (EVN) to (re-)localise FRB 20121102A and its associated persistent radio source (PRS). We confirm that the two are co-located -- improving on previous results by a factor of ~4 and constraining the FRB and PRS co-location to ~12 pc transverse offset. Over a decade, the PRS luminosity on milliarcsecond scales remains consistent with measurements on larger angular scales, showing that the PRS is still compact. We also present the detection of 18 bursts with the Nancay Radio Telescope (NRT) as part of our \'ECLAT monitoring program. These bursts, together with previously published results, show that the observed dispersion measure (DM) of FRB 20121102A has dropped by ~25 pc/cc in the past five years, highlighting a fractional decrease in the local DM contribution of>15%. We discuss potential physical scenarios and highlight possible future observations that will help reveal the nature of FRB 20121102A, which is one of only a few known FRBs with a luminous PRS.