Fast radio bursts (FRBs) are millisecond-duration, extragalactic radio flashes of unknown physical origin [1][2][3] . FRB 121102, the only known repeating FRB source [4][5][6] , has been localized to a star-forming region in a dwarf galaxy 7-9 at redshift z = 0.193, and is spatially coincident with a compact, persistent radio source 7,10 . The origin of the bursts, the nature of the persistent source, and the properties of the local environment are still debated. Here we present bursts that show ∼100% linearly polarized emission at a very high and variable Faraday rotation measure in the source frame: RM src = +1.46 × 10 5 rad m −2 and +1.33 × 10 5 rad m −2 at epochs separated by 7 months, in addition to narrow ( 30 µs) temporal structure. The large and variable rotation measure demonstrates that FRB 121102 is in an extreme and dynamic magneto-ionic environment, while the short burst durations argue for a neutron star origin. Such large rotation measures have, until now, only been observed 11,12 in the vicinities of massive black holes (M BH 10 4 M ). Indeed, the properties of the persistent radio source are compatible with those of a low-luminosity, accreting massive black hole 10 . The bursts may thus come from a neutron star in such an environment. However, the observed properties may also be explainable in other models, such as a highly magnetized wind nebula 13 or supernova remnant 14 surrounding a young neutron star. 2Using the 305-m William E. Gordon Telescope at the Arecibo Observatory, we detected 16 bursts from FRB 121102 at radio frequencies from 4.1 − 4.9 GHz (Table 1). The data recorder provided complete polarization parameters with 10.24-µs time resolution. See Methods and Extended Data Figs. 1-6 for observation and analysis details.The 4.5-GHz bursts have typical widths 1 ms, which are narrower than the 2 to 9-ms bursts previously detected at lower frequencies 5,15 . In some cases they show multiple components and structure close to the sampling time of the data. Burst #6 is particularly striking, with a width of 30 µs, which constrains the size of the emitting region to 10 km, modulo geometric and relativistic effects. Evolution in burst morphology with frequency complicates the determination 5 of dispersion measure (DM = d 0 n e (l) dl), but aligning the narrow component in Burst #6 results in DM= 559.7 ± 0.1 pc cm −3 , which is consistent 4,5,15,16 with other bursts detected since 2012, and suggests that any bona fide dispersion measure variations are at the 1% level.After correcting for Faraday rotation, and accounting for ∼2% depolarization from the finite channel widths, the bursts are consistently ∼100% linearly polarized (Fig. 1). The polarization angles PA = PA ∞ + θ (where PA ∞ is a reference angle at infinite frequency, θ = RMλ 2 is the rotation angle of the electric field vector and λ is the observing wavelength) are flat across the observed frequency range and burst envelopes (∆PA 5 • ms −1 ). This could mean that the burst durations reflect the timescale of the emission process and n...

FRB 121102 is the only known repeating fast radio burst source. Here we analyze a wide-frequency-range (1 − 8 GHz) sample of high-signal-to-noise, coherently dedispersed bursts detected using the Arecibo and Green Bank telescopes. These bursts reveal complex time-frequency structures that include sub-bursts with finite bandwidths. The frequency-dependent burst structure complicates the determination of a dispersion measure (DM); we argue that it is appropriate to use a DM metric that maximizes frequency-averaged pulse structure, as opposed to peak signal-to-noise, and find DM = 560.57 ± 0.07 pc cm −3 at MJD 57644. After correcting for dispersive delay, we find that the sub-bursts have characteristic frequencies that typically drift lower at later times in the total burst envelope. In the 1.1 − 1.7 GHz band, the ∼ 0.5 − 1-ms sub-bursts have typical bandwidths ranging from 100 − 400 MHz, and a characteristic drift rate of ∼ 200 MHz/ms towards lower frequencies. At higher radio frequencies, the sub-burst bandwidths and drift rate are larger, on average. While these features could be intrinsic to the burst emission mechanism, they could also be imparted by propagation effects in the medium local to the source. Comparison of the burst DMs with previous values in the literature suggests an increase of ∆DM ∼ 1 − 3 pc cm −3 in 4 years, though this could be a stochastic variation as opposed to a secular trend. This implies changes in the local medium or an additional source of frequency-dependent delay. Overall, the results are consistent with previously proposed scenarios in which FRB 121102 is embedded in a dense nebula.