In Italian, translating from the Italian wikipedia as accurately as I can muster,
a "complemento" is a part of a sentence (one or more words) that specify, clarify and enrich the meaning thereof.
Italian has a loooong, punctilious list of various possible types of "complemento", for example:
- I have plenty of diamonds — "complemento" of abundance
- I am short of diamonds — "complemento" of privation
- It's made of diamonds — "complemento" of matter
- Some of the diamonds are valuable — "complemento" of partition
- Each of these diamonds is valuable — "complemento" of specification
- It's worthy of diamonds — "complemento" of value
I can't find anything like this on the English wikipedia - although adjuncts sound suspiciously similar, I'd say none of these are temporal, locative, modicative, causal, instrumental, conditional or concessive - although there certainly are some that are, and not all require prepositions:
- I'm waiting there - "complemento" of being in place
- I'm going there - "complemento" of motion to place
- I'm going to Rome - "complemento" of motion to place also.
The next closest thing would be adverbial complements, but most of these aren't required for the sentence to make sense, or tied to the verb.