public class BaseController: Controller
{
    protected readonly ISomeProvider _someProvider;

    public BaseController(ISomeProvider someProvider)
    {
        this._someProvider = someProvider;
    }
}

public class HomeController : BaseController
{
    public HomeController(ISomeProvider someProvider) : base(someProvider)
    {
    }

    public IActionResult Index()
    {
        return View(_someProvider.GetSomeCollection());
    }
}