A cursory check of lga1151 motherboards does not show dvi based 2560 x 1440 resolution.
It would likely run at 1080P.
If you are considering such a monitor, you want a displayport connection which will run 4k resolution @60hz.
If you have such a monitor that you want to support, buy a discrete graphics card.
You will need dual link to go past 1080P.
Here is an inexpensive card that should do the kob.
https://www.newegg.com/Product/Product.aspx?Item=N82E16814130606