2016–17–A
Prof. Amnon Yekutieli
Course topics
Topics:
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Review of material from past semesters (the courses “Derived Categories I and II”).
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Derived categories in commutative algebra: dualizing complexes, Grothendieck’s local duality, MGM Equivalence, rigid dualizing complexes.
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Derived categories in algebraic geometry: direct and inverse image functors, global Grothendieck duality, applications to birational geometry (survey), $l$-adic cohomology and Poincare-Verdier duality (survey), perverse sheaves (survey).
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Derived categories in non-commutative ring theory: dualizing complexes, tilting complexes, derived Morita theory.
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Derived algebraic geometry: nonabelian derived categories (survey), infinity categories (survey), derived algebraic stacks (survey), applications (survey).
Requirements and grading
Topics:
-
Review of material from past semesters (the courses “Derived Categories I and II”).
-
Derived categories in commutative algebra: dualizing complexes, Grothendieck’s local duality, MGM Equivalence, rigid dualizing complexes.
-
Derived categories in algebraic geometry: direct and inverse image functors, global Grothendieck duality, applications to birational geometry (survey), $l$-adic cohomology and Poincare-Verdier duality (survey), perverse sheaves (survey).
-
Derived categories in non-commutative ring theory: dualizing complexes, tilting complexes, derived Morita theory.
-
Derived algebraic geometry: nonabelian derived categories (survey), infinity categories (survey), derived algebraic stacks (survey), applications (survey).