We introduce distributive unimodal logic as a modal logic of binary relations over posets which naturally generalizes the classical modal logic of binary relations over sets. The relational semantics of this logic is similar to the relational semantics of intuitionistic modal logic and positive modal logic, but it generalizes both of these by placing no restrictions on the accessibility relatio...

In these expository notes derived categories and functors are gently introduced, and used along with Koszul complexes to develop the basics of local cohomology. Local duality and its far-reaching generalization, Greenlees-May duality, are treated. A canonical version of local duality, via differentials and residues, is outlined. Finally, the fundamental Residue Theorem, described here e.g., for...