Static fields in a base class and derived classes

In an abstract base class if we have some static fields then what happens to them ?

Is their scope the classes which inherit from this base class or just the type from which it is inheriting (each subclass has it's own copy of the static field from the abstract base class)?

static members are entirely specific to the declaring class; subclasses do not get separate copies. The only exception here is generics; if an open generic type declares static fields, the field is specific to that exact combination of type arguments that make up the closed generic type; i.e. Foo<int> would have separate static fields to Foo<string>, assuming the fields are defined on Foo<T>.

As pointed out in other answer, the base class static field will be shared between all the subclasses. If you need a separate copy for each final subclass, you can use a static dictionary with a subclass name as a key:

class Base
{
    private static Dictionary<string, int> myStaticFieldDict = new Dictionary<string, int>();

    public int MyStaticField
    {
        get
        {
            return myStaticFieldDict.ContainsKey(this.GetType().Name)
                   ? myStaticFieldDict[this.GetType().Name]
                   : default(int);
        }

        set
        {
            myStaticFieldDict[this.GetType().Name] = value;
        }
    }

    void MyMethod()
    {
        MyStaticField = 42;
    }
}