mate desktop does not start on my ubuntu 21.10 system (lightdm doesn't start)

I installed ubuntu 21.10 and tried to replace the regular desktop by mate (I add more details below).

The current situation is, that if I boot into my ubuntu system, it displays, that it has some problem starting "light display manager" and it seems it keeps trying to start lightdm forever.

sysctrl shows the following message:

○ lightdm.service - Light Display Manager
     Loaded: loaded (/lib/systemd/system/lightdm.service; indirect; vendor preset: enabled)
     Active: inactive (dead)
       Docs: man:lightdm(1)

It also seems, that the installation uses my nvidia card, but I would rather like to use my radeon card, but I found out, that lightdm uses config file /usr/share/lightdm/lightdm.conf.d/90-nvidia.conf, which probably means, that it is trying to use the nvidia card, instead of the onboard radeon card and the nvidia card is not connected to a monitor.

Here some details about my hardware. I would like to use the radeon card for the mate desktop, because I would like to fully reserve the Nvidia card for machine learning applications. Btw. this already worked on ubuntu 20.04 and it also seemed to work for the default gnome desktop.

# sudo lshw -c video
SCSI                        
  *-display UNGEFORDERT
       Beschreibung: VGA compatible controller
       Produkt: TU106 [GeForce RTX 2070 Rev. A]
       Hersteller: NVIDIA Corporation
       Physische ID: 0
       Bus-Informationen: pci@0000:01:00.0
       Version: a1
       Breite: 64 bits
       Takt: 33MHz
       Fähigkeiten: pm msi pciexpress vga_controller cap_list
       Konfiguration: latency=0
       Ressourcen: memory:f6000000-f6ffffff memory:c0000000-cfffffff memory:d0000000-d1ffffff ioport:f000(Größe=128) memory:f7000000-f707ffff
  *-display UNGEFORDERT
       Beschreibung: VGA compatible controller
       Produkt: Raven Ridge [Radeon Vega Series / Radeon Vega Mobile Series]
       Hersteller: Advanced Micro Devices, Inc. [AMD/ATI]
       Physische ID: 0
       Bus-Informationen: pci@0000:0a:00.0
       Version: c8
       Breite: 64 bits
       Takt: 33MHz
       Fähigkeiten: pm pciexpress msi msix vga_controller bus_master cap_list
       Konfiguration: latency=0
       Ressourcen: memory:e0000000-efffffff memory:f0000000-f01fffff ioport:d000(Größe=256) memory:f7500000-f757ffff memory:c0000-dffff

What I did so far:

1. installed ubuntu desktop 21.10
2. installed mate-desktop and lightdm
3. uninstalled gnome-desktop

After that, I got the problem, that ubuntu didn't start correctly anymore

I just found out, what the reason was looking into the log using:

sudo tail -n 100 /var/log/lightdm/lightdm.log | less

There were two problems, first, the config contained xlocal (probably something is wrong in the installation routine, causing this phenomenon) and the second problem was that the config of the "arctica-greeter" was missing. I fixed the first problem by searching all config files stated by lightdm --show-config (in the source section of the output) for xlocal and then fixed it in /usr/share/lightdm/lightdm.conf.d/90-nvidia.conf. For the second problem, I just installed arctica-greeter with apt-get install arctica-greeter. Now it works :-) Maybe that helps if someone has a similar problem.

[+0.01s] WARNING: Seat type 'xlocal' is deprecated, use 'type=local' instead
[+0.01s] DEBUG: Seat seat0: Loading properties from config section Seat:*
[+0.01s] DEBUG: Seat seat0 has property CanMultiSession=no
[+0.01s] DEBUG: Seat seat0: Starting
[+0.01s] DEBUG: Seat seat0: Creating greeter session
[+0.01s] DEBUG: Seat seat0: Failed to find session configuration arctica-greeter
[+0.01s] DEBUG: Seat seat0: Failed to create greeter session
[+0.01s] DEBUG: Failed to start seat: seat0
[+0.00s] DEBUG: Logging to /var/log/lightdm/lightdm.log
[+0.00s] DEBUG: Starting Light Display Manager 1.30.0, UID=0 PID=1396