  We present the first study of the evolution of the galaxy luminosity and
stellar-mass functions (GLF and GSMF) carried out by the Dark Energy Survey
(DES). We describe the COMMODORE galaxy catalogue selected from Science
Verification images. This catalogue is made of $\sim 4\times 10^{6}$ galaxies
at $0<z\lesssim1.3$ over a sky area of $\sim155\ {\rm sq. \ deg}$ with ${\it
i}$-band limiting magnitude ${\it i}=23\ {\rm mag}$. Such characteristics are
unprecedented for galaxy catalogues and they enable us to study the evolution
of GLF and GSMF at $0<z<1$ homogeneously with the same statistically-rich
data-set and free of cosmic variance effects. The aim of this study is twofold:
i) we want to test our method based on the use of photometric-redshift
probability density functions against literature results obtained with
spectroscopic redshifts; ii) we want to shed light on the way galaxies build up
their masses over cosmic time. We find that both the ${\it i}$-band galaxy
luminosity and stellar mass functions are characterised by a double-Schechter
shape at $z<0.2$. Both functions agree well with those based on spectroscopic
redshifts. The DES GSMF agrees especially with those measured for the GAlaxy
Mass Assembly and the PRism MUlti-object Survey out to $z\sim1$. At $0.2<z<1$,
we find the ${\it i}$-band luminosity and stellar-mass densities respectively
to be constant ($\rho_{\rm L}\propto (1+z)^{-0.12\pm0.11}$) and decreasing
($\rho_{\rm Mstar}\propto (1+z)^{-0.5\pm0.1}$) with $z$. This indicates that,
while at higher redshift galaxies have less stellar mass, their luminosities do
not change substantially because of their younger and brighter stellar
populations. Finally, we also find evidence for a top-down mass-dependent
evolution of the GSMF.
