Is there a remote desktop app for iPad that works well with a bluetooth keyboard? I am a programmer and I like my new iPad because its screen is fantastic. 

I am eagerly awaiting the arrival of the Adonit Writer Plus for the new iPad in the mail. 

Here's what I want to know: Which iPad remote desktop apps have the best bluetooth keyboard support? The keyboard has most of the standard keys and I'd like to be able to issue Ctrl, Alt, Windows (and the *nix and Mac equivalents) keypresses to the host machine seamlessly. This will allow me to use a proper IDE (among many other things) when on-the-go. 

I'll of course be able to get light-duty work done in the wonderful Textastic app when not connected. 

In addition to this can anybody tell me if there is the possibility of running a full 2048x1536 resolution remote desktop session? It will probably not prove useful due to monstrous network lag. But it would be cool.
Screens is probably the best app for that. Works with OS X builtin screen sharing but can connect to all VNC sources. It has a really smart way of translating touch to mouse events but also has bluetooth keyboard support, including modifier keys. And tons of other features. It runs 2560x1440 sessions smoothly on my side, you can pinch-zoom to get the scale you like.