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Taiwan Math School: Derived Category in Algebraic Geometry
10:00 - 12:00, November 3, 2017 (Friday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Taiwan Math School: Derived and Homological Algebraic Geometry
Jungkai Chen (National Taiwan University & NCTS)

Course Description: 

Phase 1: Introductory to Abstract Algebra Constructions

  • Homological Algebra: Ring and module, exact sequences, Hom and tensor, injective/projective/flat, free resolution, derived functors (Ext and Tor). 
  • Commutative Algebra: Local rings, Spec, 
  • Category Theory: Abelian Category, Localization construction, Triangulated Category

Phase 2: Introductory to Algebraic Geometry

  • Algebraic Geometry: Varieties, Scheme, Sheaves, and cohomology theory
  • Cohomology and base change theorem

Phase 3: Introductory to Derived Category

  • Category of sheaves
  • Derived Category in Algebraic Geometry 
  • Semi-orthogonal decomposition
  • Fourier-Mukai transforms 

Phase 4: Advanced Topics

  • Fourier-Mukai transforms on Abelian varieties 
  • Derived Category of Toric Varieties
  • Bridgeland stability conditions

Time: From 10/27 to 12/15(Every Friday) 10:00-12:00


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