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Ludicrous speed through scheme basics

Nov 23
Nov 30
Dec 2
Projective spaces

Past topics

Generation and representability

Nov 4
Serre functors
Nov 9
Brown representability
Nov 11
Strong generation and ghosts
Nov 16
Strong generation and saturation
Nov 18
Examples of strong generation

Semi-orthogonal decompositions

Oct 26
SODs and upper triangular algebras
Oct 28
Properties of SODs
Nov 2
Mutations and braid group actions

Derived Morita equivalences, dg-algebras, and integral transforms

Oct 12
Derived categories of dg-modules
Oct 14
Derived Morita equivalences and integral transforms
Oct 19
More on kernels, homological smoothness and properness
Oct 21
A look ahead to geometry

Compactly generated triangulated categories

Oct 5
Compact generators and resolutions

The derived category and derived functors

Sept 16
Triangulated categories
Sept 21
K-projectives and K-injectives
Sept 23
Derived categories
Sept 28
Derived functors
Sept 30
Derived tensor and Hom

Abelian categories and chain complexes

Sept 7
Abelian categories and (half) exact functors
Sept 9
Exactness for $\text{Hom}$ and $\otimes$: projectives, injectives, and flat modules
Sept 14
Homotopy category of chain complexes


Aug 24
Definitions of categories and examples
Aug 26
Functors, natural transformations, and equivalences
Aug 31
Sept 2
Representable functors and Yoneda