Formation of the Ablative Absolute
When we form the ablative absolute, we have two words that are put in the ablative case. Next, we finish the sentence by connecting the two ablative case words, though the connection is grammatically loose.
The ablative absolute can have three different sentence formations, where the ablative case words are either:
1) a substantive and a participle,
2) two substantives
3) a substantive and an adjective.
The first sentence construction, a substantive and a participle, is the most commonly used one; the participle must match the gender, number and case of the substantive. The same principle applies to the third sentence formation, the adjective must match the gender, number and the case of the substantive. Let's look at examples of each of the sentences (examples are from "Smith's First Year Latin"):
Signō datō, oppidum oppugnāvērunt. (sentence type one)
(The signal having been given) When the signal had been given, they attacked the town.
Caesare imperātōre, ad victōriam exercitus dūcētur. (sentence type two)
If Caesar is general, the army will be led to victory.
Perīculō magnō, Caesar signum dedit. (sentence type three)
Since the danger was great, Caesar gave the signal.