paging while viewing pdf's

i think it would be great if it was easier to page through a pdf while in split view mode…
intuitively it would be
click on pdf in file list
tab to pdf content
page up/down (or sideways arrows for pg up/down)
up down arrows for line by line scrolling

similar functionalty for text etc docs owudl be fabbo.!

Here is how I do it:

click on pdf in file list [color=red]Same
tab to pdf content [color=red]Opt-Tab
page up/down (or sideways arrows for pg up/down) [color=red]Cmd-Right/Left arrow to page forward/back
up down arrows for line by line scrolling [color=red]Same. Also, Cmd-Up arrow to go to the first page, Cmd-Down arrow to go to the last page.