Arcologies are generally fully contained and self-sufficient facilities. They include onsite living, food production, and waste processing, as well as the real focal point: whatever work is being done there. They are generally only maintained by Corps and Megacorps due to their extreme expense and size. They sometimes function as a sort of prison for the employees-being self-sufficient, they don’t need to placed near major cities or even large farm areas to secure supply line, so the corp is able to have near total control over the resident employees lives.
The best known arcology is the (now-empty) Renraku site located near Seattle. The on-site central A.I. (Deus) achieved autonomy and went berserk, sealing off the arcology. The next anyone heard, the A.I. had escaped, after having carried out some disturbing experiments on it’s captives. Deus later helped trigger the second great matrix crash, in 2064, leading to a rearranging of corporate powers and the establishment of the wireless world.
Aquacologies (full or partial immersion arcologies) are also becoming more popular on Earth, although they obviously don’t exist on Mars, due to the lack of sufficient standing water. The largest is the city of LA in CalFree, which flooded heavily after the earthquakes in the year of the comet. Most of the wealthier areas were already walled off, to prevent such an eventuality, but many of the slums were heavily damaged or destroyed. The city government took the chance to rebuild “better” and is now mostly self-sufficient, although still open to travel and trade, unlike most arcologies, which are closed facilites.
The team managed to extract a sentient A.I. from a Mars Renraku arcology, and have been helping the A.I., named Daedelus, on various jobs. Renraku is presumably looking for Deadelus fairly thoroughly, as many people would panic to hear of an escaped A.I., after the disastrous results that occurred in 2064.