  Searches for scalar leptoquarks pair-produced in proton-proton collisions at
$\sqrt{s}=13$ TeV at the Large Hadron Collider are performed by the ATLAS
experiment. A data set corresponding to an integrated luminosity of 36.1
fb$^{-1}$ is used. Final states containing two electrons or two muons and two
or more jets are studied, as are states with one electron or muon, missing
transverse momentum and two or more jets. No statistically significant excess
above the Standard Model expectation is observed. The observed and expected
lower limits on the leptoquark mass at 95% confidence level extend up to 1.29
TeV and 1.23 TeV for first- and second-generation leptoquarks, respectively, as
postulated in the minimal Buchm\"uller-R\"uckl-Wyler model, assuming a
branching ratio into a charged lepton and a quark of 50%. In addition,
measurements of particle-level fiducial and differential cross sections are
presented for the $Z\rightarrow ee$, $Z\rightarrow\mu\mu$ and $t\bar{t}$
processes in several regions related to the search control regions. Predictions
from a range of generators are compared with the measurements, and good
agreement is seen for many of the observables. However, the predictions for the
$Z\rightarrow\ell\ell$ measurements in observables sensitive to jet energies
disagree with the data.
