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Last updated:

November 7, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology.

Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

Course Curriculum

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

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Massachusetts Institute of Technology
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