MA 311: Algebraic Geometry II
Credits: 3:0
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Sheaves of differentials.
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Background on homological algebra : resolutions, derived functors, $\delta$-categories.
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Triangulated categories, Derived categories of abelian categories.
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Injective and flasque resolutions.
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Cohomology of sheaves of abelian groups
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Vanishing theorems for cohomology
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Serre’s criterion for affineness
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Čech cohomology
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Cohomology of projective space, twisting by Serre sheaves
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$Ext$ and $Tor$ for sheaves
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Serre duality theorem
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Schemes as functors of points, the idea of stacks
Suggested books and references:
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977.
- 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.