Can the Green Lanterns arrest people on planets?

Question

Can they arrest someone on a planet or do they have to make arrests in space? Do they have that kind of authority?

Answer 1

It varies from system to system. Some star systems recognize the Corps as a peacekeeping force and afford them the respect they would a law enforcement official or first responder. Presumably, any planet or system who actively requests the aid of the Corps would afford them said respect.

Some systems (the Vega system, for example) have specifically banned them from operating them in their zone of control. Earth of the 30th century, the era of the legion of Super heroes, had banned Lanterns for many years.

It's assumed many systems don't actually have any knowledge of them at all, and one one arrives to help with an emergency or other reason, decisions are made on the fly.

Answer 2

They police everywhere.

Quoting from this answer:

Their jurisdiction (prior to the new 52 that started this month) was the entire known universe*. The Guardians split the universe into 3600 sectors with Oa at the center, and each sector being a wedge radiating out from Oa (this is based on a map they had in a Green Lantern special issue a few years ago). I don't think there's a known distance between Earth and Oa.

And Wikipedia says that this:

The Corps is an organization of 7200+ Green Lanterns (the old Corps was composed of 3600) who are chosen by the ring for being able to overcome great fear, with two assigned to each sector of space that require the protection of more than one Green Lantern (Earth, home to Hal Jordan and John Stewart, is in Sector 2814). Heavily populated Sectors like 2814 can have several Lanterns. While the primary Lanterns of Sector 2814 are Hal Jordan and John Stewart, Kyle Rayner and Guy Gardner call Earth home, but are stationed on Oa, first as teachers, and then specially assigned to cases that are too difficult for the average lantern.

This would presumably include both planets and space - seeing as they're pretty much policing the entire universe, they would indeed be able to arrest people on planets.