Timeline for Computing RHom of skyscraper sheaves / sheaves of subvarieties
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2023 at 6:10 | comment | added | Sasha | @Cranium Clamp: I think you can find an answer in the book of Daniel Huybrechts. | |
| Feb 8, 2023 at 6:09 | comment | added | Sasha | @D.-C.Cisinski: I guess the OP is about the derived category of coherent sheaves, and on it the functor $i_*$ is not fully faithful. | |
| Feb 8, 2023 at 5:26 | comment | added | D.-C. Cisinski | For any closed immersion $i\colon Y\to X$ any complexes of sheaves $F$ and $G$ on $Y$, we have $RHom(F,G)\cong RHom(i_*F,i_*G)$ in the derived category. This holds because $i_*$ is fully faithful on derived categories, which follows from the fact that both $i_*$ and $i^*$ are exact on ordinary sheaves and $i^*i_*F\cong F$ for any sheaf $F$. This is purely topological and has nothing to do with any regularity conditions. | |
| Feb 8, 2023 at 2:29 | history | asked | Cranium Clamp | CC BY-SA 4.0 |