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Etale Cohomology
Before this, knowHigher Math: Algebraic Number Theory and Class Field TheoryGalois Cohomology and DualitySheaves and Algebraic Geometry
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Some version of Poincare duality—perhaps something about perfect intersection pairings useful for extracting the intersection of diagonal with the graph of a morphism—is apparently used to prove the Grothendieck–Lefschetz trace (fixed point) formula. Reference: Frietag–Kiehl.
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Benson Farb, Representation Stability