During an upgrade my kernel got corrupted and the server went down. Thankfully OVH offers a Netboot and Network mode. I used the network option and chose one of the available kernels, which dropped me in one of my own installation and executed the following:

To reinstall the current linux kernel:

List available kernels

apt-cache search linux-image

Reinstall the kernel:

apt-get install --reintall linux-image-3.16.0-4-amd64

Update grub configuration:

update-grub

And hard reboot server