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 $sim 4times 10^{6}$ galaxies at $0<zlesssim1.3$ 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 $zsim1$. At $0.2<z<1$, we find the ${it i}$-band luminosity and stellar-mass densities respectively to be constant ($rho_{rm L}propto (1+z)^{-0.12pm0.11}$) and decreasing ($rho_{rm Mstar}propto (1+z)^{-0.5pm0.1}$) 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.
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