Hibernate mode uses the hiberfil.sys file to store the current state (memory) of the PC, and since it's managed by Windows, you can't delete the file.

Ran a antivirus program and it said that hiberfil.sys and pagefile.sys are infected by a trojan. The program couldn't remove them since i guess they are read only. Should i remove them manually ...

Fast Startup saves the system kernel and drivers to the Windows hibernation file called Hiberfil.sys, allowing for quicker boot times.

This file can become corrupt and cause Hibernate not to work properly. To fix this problem, you will need to delete the hiberfil.sys file and let Windows rebuild it.