Jorge Vitória "A tour of finite/telescope-type results in representation theory."

How much information can we get on the category of all modules from the subcategory of finitely presented modules? To which extent is the structure of the derived category of modules determined by its subcategory of compact objects? How much does the grip that finitely presented/compact objects yield over the structure of the whole category depend on the ring at study?

In this series of lectures we survey some partial answers to these general questions, both in the category of modules over a ring and in its derived category.