Mathematics

**MTH ****624: An introduction to schemes and cohomology **** ****(4)**

Prerequisites: MTH 415

Desirable: MTH 517

**Course contents:**

Basics of Category theory , Sheaves , Schemes, Properties of Schemes, Separated and Proper Morphisms, Sheaves of Modules, Divisors, Projective Morphisms, Differentials, Derived Functors, Cohomology of Sheaves, Cohomology of a Noeitherian Affine Schemes, Cech Cohomology, Cohomology of Projective spaces, Ext group and Scheves , Serre Duality theorem (statement only), Flat Morphisms and Smooth Morphisms

*Suggested Books*:

- David Mumford,The Red Book of Varieties and Schemes, Springer; 2nd exp. ed. 1999.
- Hartshorne, Robin. Algebraic Geometry. New York, NY: Springer, 1997.
- Phillip Griffiths, Joseph Harris, Principles of Algebraic Geometry, Wiley-Interscience; 1st edition 1994.

*References*:

- David Eisenbud, The Geometry of Schemes: 197, Springer 2002
- Ulrich GoĢrtz , Torsten Wedhorn, Geometry I: Schemes: With Examples and Exercises,Vieweg+Teubner Verlag,2010
- Shafarevich, Igor .R ,Basic Algebraic Geometry 2 : Schemes and Complex Manifolds, Springer Nature (SIE), 2014

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