Grothendieck Duality
Grothendieck duality relates derived pushforward to a twisted inverse-image functor and dualizing complexes. Use the stated theory for finite type separated schemes over a Noetherian base to organize the proper-map duality formula and its smooth proper specialization.
Before opening the references
Scheme · Noetherian Commutative Ring · Adjunction · Ext Group of Modules · Chain Complex of Modules
Where to read
Start here: The Stacks Project — A duality theory
The Stacks Project Authors · Online reference · English · Free full text
Section 48.19, numbered assertions (1)–(4) and (9), followed by the discussion of determining upper shriek
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Algebraic Geometry in the library · Preparation and skip guidance