  A precise knowledge of the quark and gluon structure of the proton, encoded
by the parton distribution functions (PDFs), is of paramount importance for the
interpretation of high-energy processes at present and future lepton-hadron and
hadron-hadron colliders. Motivated by recent progress in the PDF determinations
carried out by the CT, MSHT, and NNPDF groups, we present an updated
combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo
combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its
Hessian reduction or its replica compression. Extensive benchmark studies are
carried out in order to disentangle the origin of the differences between the
three global PDF sets. In particular, dedicated fits based on almost identical
theory settings and input datasets are performed by the three groups,
highlighting the role played by the respective fitting methodologies. We
compare the new PDF4LHC21 combination with its predecessor, PDF4LHC15,
demonstrating their good overall consistency and a modest reduction of PDF
uncertainties for key LHC processes such as electroweak gauge boson production
and Higgs boson production in gluon fusion. We study the phenomenological
implications of PDF4LHC21 for a representative selection of inclusive,
fiducial, and differential cross sections at the LHC. The PDF4LHC21 combination
is made available via the LHAPDF library and provides a robust, user-friendly,
and efficient method to estimate the PDF uncertainties associated to
theoretical calculations for the upcoming Run III of the LHC and beyond.
