I agree with Paul that 'today' is not a subject complement. Compare
these sentences:

1. The exam was today.
2. The exam was easy today.
3. The exam took place today.
4. *The exam took place easy today.

'Took place' certainly is not a copular verb. It takes 'today' as a
temporal modifier.

I disagree, however, that 'given' is 'implied' or 'understood'. If you
don't see it, maybe it isn't there (a favorite quote -- oops, quotation
-- from an ancient TV sitcom, F Troop). Something implied or understood
is not grammatically a part of the sentence that is actually said.
That's what makes it implied or understood -- it has to be gotten, not
from the sentence, but from the discourse context.

Plenty of expressions are short forms of longer expressions. That's
probably how we got from 'The exam is on Thursday' to 'The exam is
Thursday'. Humans love to minimize language effort and will do so
whenever the discourse context allows recovery of the omitted meaning.
Some meanings are so easily recoverable, it becomes optional to put them
into words at all. Then a new way of structuring the message comes into
being. The old way may die out altogether.

I believe that the verb 'be' simply accepts temporal complements, like
many other English verbs. We can say

5. When was the concert?
6. When will the wedding be?
7. When is your party?

'Be' has a sense that is synonymous with 'happen, occur, take place'.