By Brian Conrad
Grothendieck's duality idea for coherent cohomology is a basic device in algebraic geometry and quantity thought, in parts starting from the moduli of curves to the mathematics idea of modular kinds. provided is a scientific evaluation of the complete concept, together with many simple definitions and an in depth examine of duality on curves, dualizing sheaves, and Grothendieck's residue image. alongside the best way proofs are given of a few typical foundational effects which aren't confirmed in current remedies of the topic, akin to the final base swap compatibility of the hint map for correct Cohen-Macaulay morphisms (e.g., semistable curves). this could be of curiosity to mathematicians who've a few familiarity with Grothendieck's paintings and want to appreciate the main points of this thought.
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