List questions from derived-categories | MathQa

A an Abelian category, define the derived category as $D(A) = Ch(A)[Qiso^{-1}]$. Why do homotopic maps become equal?

Published on 13 Jan 2025 - 0:43

A map of complexes which is zero on cohomology but not zero in $D(\mathcal{A})$

Published on 13 Jan 2025 - 0:36

Calculate $\operatorname{RHom}$ in a the derived category of graded $\mathbb{C}[x]$-Modules

Published on 13 Jan 2025 - 0:39

Yoneda extensions and $\operatorname{Ext}$ functor.

Published on 13 Jan 2025 - 0:20

Bounded derived category and hereditary categories

Published on 13 Jan 2025 - 0:23

If $D$ is a triangulated category, and $E_i$ is a set of generators, then $D$ is equivalent to $D(End(\oplus E_i))$?

Published on 13 Jan 2025 - 0:43

Cohomologies with line bundle vs. coherent coefficients

Published on 13 Jan 2025 - 0:27

A left exact functor preserves quasi-isomorphisms between acyclic complexes

Published on 13 Jan 2025 - 0:37

A cochain complex with finitely generated cohomology is quasi-isomorphic to a cochain complex of finitely generated module

Published on 13 Jan 2025 - 0:44

Image of a line bundle on an elliptic curve under Fourier-Mukai transform

Published on 13 Jan 2025 - 0:35