Variable stars in two open clusters within the Kepler/K2-Campaign-0 field: M35 and NGC 2158

We present a multi-year survey aimed at collecting (1) high-precision (~5 milli-mag), (2) fast-cadence (~3 min), and (3) relatively long duration (~10 days) multi-band photometric series. The goal of the survey is to discover and characterize efficiently variable objects and exoplanetary transits in four fields containing five nearby open clusters spanning a broad range of ages. More in detail, our project will (1) constitute a preparatory survey for HARPS-N@TNG, which will be used for spectroscopic follow-up of any target of interest that this survey discovers or characterizes, (2) measure rotational periods and estimate the activity level of targets we are already monitoring with HARPS and HARPS-N for exoplanet transit search, and (3) long term characterization of selected targets of interest in open clusters within the planned K2 fields. In this first paper we give an overview of the project, and report on the variability of objects within the first of our selected fields, which contains two open clusters: M 35 and NGC 2158. We detect 519 variable objects, 273 of which are new discoveries, while the periods of most of the previously known variables are considerably improved.