Each Corps represents a color and an emotion that goes with it. Red = Rage, Orange = Avarice (Greed), Yellow = Fear, Green = Willpower, Blue = Hope, Indigo = Compassion, Violet = Love, Black = Death, White = Life. The Central Power Battery of each color houses the single color light for that Emotion. The Ring that each Corps Member wears draws it's power from the Central Power Battery or a smaller battery assigned to the Corps Member. This power allows varying abilities such as flight, construct projection (physical creations made out of light that can be anything the wielder imagines), and enhanced stamina. Each cache will focus on just one of these corps and will involve some math and research skills. The hide shouldn't be too hard either. Have fun and ask any questions you'd like!
According to DC continuity, before recruiting sentient beings to the Green Lantern Corps, the Guardians formed a robotic army called the Manhunters to maintain order across the universe. After eons of service, the renegade Guardian Krona altered their central programming, leading them to believe that the only way of maintaining order was to completely rid the universe of all known life. Sector 666 falls victim to this new philosophy when the Manhunters slaughter all but five of its inhabitants. The five survivors become known as the Five Inversions: a terrorist cell bent on the destruction of the Guardians of the Universe. They are incarcerated on the planet Ysmault, where one member, Atrocitus, is so consumed by his rage that it results in the formation of the first red power battery. (From Wikipedia)
Each Corps has an Oath it states from time to time, usually to recharge their ring. This is the Red Lantern Oath:
"With blood and rage of crimson red,
Ripped from a corpse so freshly dead,
Together with our hellish hate,
We'll burn you all--that is your fate!"
In order to find this cache, you will need to do some math. Find what Space Sector each member of the Corps is from or assigned to protect (these may be the same number or could be different). Replace their name with the Space Sector Number and apply the following equations to the last three digits of the coordinates above:
North: + Laira + Bleez + Vice - 58
West: - (Zillius Zox - Dex-Starr) + Veon + 32
Make sure to make note of the clue on the cache log in order to find the War of Light / Blackest Night Cache!