By Leovigildo Alonso Tarrio, Ana Jeremias Lopez, Joseph Lipman
This quantity comprises 3 papers at the foundations of Grothendieck duality on Noetherian formal schemes and on not-necessarily-Noetherian traditional schemes. the 1st paper offers a self-contained therapy for formal schemes which synthesizes numerous duality-related themes, reminiscent of neighborhood duality, formal duality, residue theorems, dualizing complexes, and so forth. incorporated is an exposition of homes of torsion sheaves and of limits of coherent sheaves. A moment paper extends Greenlees-May duality to complexes on formal schemes. This theorem has vital functions to Grothendieck duality. The 3rd paper outlines tools for taking away the Noetherian hypotheses.A easy function is performed by means of Kiehl's theorem declaring conservation of pseudo-coherence of complexes lower than right pseudo-coherent maps. This paintings supplies an in depth advent to Grothendieck Duality, unifying assorted issues. for instance, neighborhood and international duality seem as various situations of an analogous theorem. Even for usual schemes, the method - encouraged by means of that of Deligne and Verdier - is significantly extra common than the single in Hartshorne's vintage ""Residues and Duality."" additionally, shut realization is paid to the category-theoretic points, specially to justification of all wanted commutativities in diagrams of derived functors.