In C# 4.0, is it possible to derive a class from a generic type parameter?

Generic types in C# are not C++ templates; remember, a generic type must work for all possible type arguments. A template need only work for the constructions you actually make.

This question is a duplicate; see my answer to

Why cannot C# generics derive from one of the generic type parameters like they can in C++ templates?

for more thoughts on this. Basically, the short answer is that the considerable costs do not outweigh the small benefits of the feature. If you don't like that answer, see my second answer:

Why cannot C# generics derive from one of the generic type parameters like they can in C++ templates?

And if you don't like that answer either, see the follow-up question:

What are the good reasons to wish that .NET generics could inherit one of the generic parameter types?

No, this is not possible. For example, take a type that is declared sealed. You can't inherit from that class, and there is no constraint to limit to non sealed types, ergo trying to inherit from it via a generic parameter is impossible.