Math M701: The Language of Algebraic Geometry
This course is intended as an introduction to the language of algebraic geometry
developed by Grothendieck and others, especially sheaves, schemes, and
(time permitting) cohomology. Topics will include the Zariski topology,
Spec and Proj constructions, finiteness, compactness, and separation conditions,
sheaves of functions, coherent and quasi-coherent sheaves of modules,
divisors and line bundles, tangent and cotangent bundles, and Čech cohomology.
Prerequisites: M501-502. Differential geometry, algebraic topology,
and complex analysis may be helpful but are not required.
Recommended text: Robin Hartshorne: Algebraic Geometry.
Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977.