What options are available for ventilation above a stove?
OK, my understanding is that you have a stove on a section of counter that doesn't have a wall immediately behind it. This could result in a "peninsula" design, or an outright "island".

Either way, what you want is an "island-mount vent hood". They're designed to install in the ceiling instead of against a wall, for stoves that are out in the middle of a kitchen layout for whatever reason.

Now, most of these vent hoods will have some drop from the ceiling. This is because the further away the fume hood is, the larger it has to be in order to catch the rising steam/smoke from whatever's on the stove. You generally want between 3 and 4 feet clearance between the stove and hood, with a minimum of 30" required by most building codes. With a standard 36" countertop and an 8ft ceiling, a flush-mounted vent hood would be about 5 1/2' from the surface of the stove, which is a bit high. A 9' ceiling would put the hood over 6' off the stove surface. 

So, while there are designs that minimize the profile of the hood, and you can usually install them high enough that they're above eye level (though I'm 6', and most installations I've seen have been at or below my eye level), I don't think a ceiling mount will be feasible, as you will need a commercial-size hood to have the area necessary to catch the column of smoke at that height.