### MA 311: Algebraic Geometry II

#### Credits: 3:0

• Sheaves of differentials.

• Background on homological algebra : resolutions, derived functors, $\delta$-categories.

• Triangulated categories, Derived categories of abelian categories.

• Injective and flasque resolutions.

• Cohomology of sheaves of abelian groups

• Vanishing theorems for cohomology

• Serre’s criterion for affineness

• \v{C}ech cohomology

• Cohomology of projective space, twisting by Serre sheaves

• $Ext$ and $Tor$ for sheaves

• Serre duality theorem

• Schemes as functors of points, the idea of stacks

#### Suggested books and references:

1. Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977.
2. Robin Hartshorne, Residues and duality, Lecture notes of a seminar on the work of A.~Grothendieck, given at Harvard 1963/64. With an appendix by P.~Deligne. Lecture Notes in Mathematics, No. 20 Springer-Verlag, Berlin-New York 1966.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 26 Jun 2019