  We present a lattice QCD determination of the vector and scalar form factors
of the kaon semileptonic decay $K \to \pi \ell \nu$, which is relevant for the
determination of the CKM matrix element $|V_{us}|$ from experimental data. Our
results are based on the gauge configurations produced by the European Twisted
Mass Collaboration with Nf = 2+1+1 dynamical fermions. We simulated at three
different values of the lattice spacing and with pion masses as small as 210
MeV. Our estimate for the vector form factor at zero 4-momentum transfer is
$f_+(0) = 0.9709 (46)$, where the uncertainty is both statistical and
systematic. By combining our result with the latest experimental value of
$f_+(0)|V_{us}|$ we obtain $|V_{us}| = 0.2230 (11)$, which satisfies the
unitarity constraint of the Standard Model at the permille level using the
updated determination of $|V_{ud}|$ coming from superallowed nuclear $\beta$
decays. We present also the momentum dependence of the vector and scalar form
factors in the whole range of values of the squared 4-momentum transfer
measured in $K_{\ell 3}$ decays, obtaining a good agreement with the
experimental data.
