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This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology.
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English
English [CC]
FREE
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Description
Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.
Course content
- 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
Instructor
Massachusetts Institute of Technology
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1916
1520
