.NET is not just the standard library. The standard library is called the FCL (Framework Class Library). It's also the tools needed to create and run MSIL (.NET bytecode) applications, such as the CLR (Common Language Runtime).
it's called "the DotNET framework" - so its name already implies that there's more to it than just the base for C# or ASP
I don't know DotNET, but by the last post it seems to be the name for the whole environment like lang spec, tool-chain, runtime, etc. So, by this, I don't see where such thing could be for Java the way you try to see. But you could try it the other way around: as C# and ASP use DotNET, the same is true for Java, Scala and Groovy using the, well, I would call it "the Java framework", although this still doesn't fit perfect.
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