Mart got it right with the 'new' keyword. 
I actually got here because I needed this type of functionality and Mart's solution works fine. In fact I took it one better and made my base class method abstract to force the programmer to supply this field.
My scenario was as follows: 
I have a base class HouseDeed. Each House type is derived from HouseDeed must have a price.
Here is the partial base HouseDeed class:
public abstract class HouseDeed : Item
{
    public static int m_price = 0;
    public abstract int Price { get; }
    /* more impl here */
}
Now lets look at two derived house types:
public class FieldStoneHouseDeed : HouseDeed
{
    public static new int m_price = 43800;
    public override int Price { get { return m_price; } }
    /* more impl here */
}
and...
public class SmallTowerDeed : HouseDeed
{
    public static new int m_price = 88500;
    public override int Price { get { return m_price; } }
    /* more impl here */
}
As you can see I can access the price of the house via type SmallTowerDeed.m_price, and the instance new SmallTowerDeed().Price
And being abstract, this mechanism nags the programmer into supplying a price for each new derived house type.
Someone pointed how 'static virtual' and 'virtual' are conceptually at odds with one another. I disagree. In this example, the static methods do not need access to the instance data, and so the requirements that (1) the price be available via the TYPE alone, and that (2) a price be supplied are met.