Context. Theoretical scenarios propose that high-mass stars are formed by disk-mediated accretion. Aims. To test the theoretical predictions on the formation of massive stars, we wish to make a thorough study at high-angular resolution of the structure and kinematics of the dust and gas emission toward the high-mass star-forming region G35.03+0.35, which harbors a disk candidate around a B-type (proto)star. Methods. We carried out ALMA Cycle 0 observations at 870 μm of dust of typical high-density, molecular outflow, and cloud tracers with resolutions of <0. 5. Complementary Subaru COMICS 25 μm observations were carried out to trace the mid-infrared emission toward this star-forming region. Results. The submillimeter continuum emission has revealed a filamentary structure fragmented into six cores, called A-F. The filament could be in quasi-equilibrium taking into account that the mass per unit length of the filament, 200-375 M /pc, is similar to the critical mass of a thermally and turbulently supported infinite cylinder, ∼335 M /pc. The cores, which are on average separated by ∼0.02 pc, have deconvolved sizes of 1300-3400 AU, temperatures of 35-240 K, H 2 densities >10 7 cm −3 , and masses in the range 1-5 M , and they are subcritical. Core A, which is associated with a hypercompact Hii region and could be the driving source of the molecular outflow observed in the region, is the most chemically rich source in G35.03+0.35 with strong emission of typical hot core tracers such as CH 3 CN. Tracers of high density and excitation show a clear velocity gradient along the major axis of the core, which is consistent with a disk rotating about the axis of the associated outflow. The PV plots along the SE-NW direction of the velocity gradient show clear signatures of Keplerian rotation, although infall could also be present, and they are consistent with the pattern of an edge-on Keplerian disk rotating about a star with a mass in the range 5-13 M . The high t ff /t rot ratio for core A suggests that the structure rotates fast and that the accreting material has time to settle into a centrifugally supported disk. Conclusions. G35.03+0.35 is one of the most convincing examples of Keplerian disks rotating about high-mass (proto)stars. This supports theoretical scenarios according to which high-mass stars, at least B-type stars, would form through disk-mediated accretion.