  Results of a search for ultra-high-energy neutrinos with the Pierre Auger
Observatory from the direction of the blazar TXS 0506+056 are presented. They
were obtained as part of the follow-up that stemmed from the detection of
high-energy neutrinos and gamma rays with IceCube, \textit{Fermi}-LAT, MAGIC,
and other detectors of electromagnetic radiation in several bands. The Pierre
Auger Observatory is sensitive to neutrinos in the energy range from 100 PeV to
100 EeV and in the zenith angle range from $\theta=60^\circ$ to
$\theta=95^\circ$, where the zenith angle is measured from the vertical
direction. No neutrinos from the direction of TXS 0506+056 have been found. The
results were analyzed in three periods: One of 6 months around the detection of
IceCube-170922A, coinciding with a flare period of TXS 0506+056, a second one
of 110 days during which the IceCube collaboration found an excess of 13
neutrinos from a direction compatible with TXS 0506+056, and a third one from
2004 January 1 up to 2018 August 31, over which the Pierre Auger Observatory
has been taking data. The sensitivity of the Observatory is addressed for
different spectral indices by considering the fluxes that would induce a single
expected event during the observation period. For indices compatible with those
measured by the IceCube collaboration the expected number of neutrinos at the
Observatory is well-below one. Spectral indices as hard as 1.5 would have to
apply in this energy range to expect a single event to have been detected.
