Open Problem Garden and Wikipedia are good resources for more or less famous open problems. But many mathematicians will be happy with more specialized problems. They may want to find a research theme, e.g. for their PhD thesis, or they may have one, and want to connect their work to other problems, to find applications. Or they may simply want to check if something is already done about a particular question.

So, I would like to ask you (I apologize in advance if the question is not appropriate for MO):

can you suggest some links to other compilations of open problems, even if they are very specialized and not as famous?

Please note that I would like it to be large and specialized, not to contain only famous conjectures. I think each subject in mathematics has many such open problems. It would be useful to be maintained such a list, containing problems classified on subject. It would be useful to be able to check there if new progress was made, who is working to those particular problems, and how important are these problems (e.g. rated as in Open Problem Garden).

Thank you.