Nvidia Shield TV Mirroring different resolution

[HarisP]

I've got a 3440x1440 ultrawide monitor on my PC, and I want to be able to access my PC from the TV in my living room (3840x2160).

 

My PC and TV are in different rooms, so the best way I could think of to connect my TV to the PC would be to use a device like the Nvidia Shield to mirror the PC to my TV. I expect that I may run into a problem though, since they're 2 different resolutions and different aspect ratios.

 

My question is: do I have any way to access my PC from an Nvidia shield TV at the TV's native resolution/framerate (4k 120Hz)? If Nvidia shield isn't the way to do this, is there another way? I know the simplest solution is to run an HDMI cable from my PC to the TV, but since they're in different rooms, this is not an option.

 

If it's relevant, my graphics card is a GTX 1070, but I may be upgrading to a 3080 soon.

 

Thanks in advance!