By Brian Conrad
Grothendieck's duality idea for coherent cohomology is a basic instrument in algebraic geometry and quantity idea, in components starting from the moduli of curves to the mathematics thought of modular varieties. awarded is a scientific review of the total conception, together with many easy definitions and an in depth learn of duality on curves, dualizing sheaves, and Grothendieck's residue image. alongside the best way proofs are given of a few widespread foundational effects which aren't confirmed in present remedies of the topic, akin to the final base switch 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 need to appreciate the main points of this concept.
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