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Algebraic Geometry Lecture Notes by Prof. Kiran Kedlaya

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Algebraic Geometry Lecture Notes written by Prof. Kiran Kedlaya . This is an other book of mathematics cover the following topics.

  • Introduction and overview
  • Basics of category theory
  • Sheaves, Abelian sheaves, Schemes,
  • Morphisms of schemes, Sheaves of modules
  • More properties of morphisms
  • Projective morphisms, part 1, Projective morphisms, part 2
  • More properties of schemes
  • Flat morphisms and descent
  • Differentials, Divisors, Divisors on curves
  • Homological algebra, Sheaf cohomology
  • Cohomology of quasicoherent sheaves, Cohomology of projective spaces
  • Hilbert polynomials, GAGA, Serre duality for projective space
  • Dualizing sheaves and Riemann-Roch,
  • Cohen-Macaulay schemes and Serre duality
  • Higher Riemann-Roch, Étale cohomology

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