In the following sentence, shouldn't we be using "bleiben" instead? Because "wir bleiben" and hence "uns bleiben"?
Uns bleibt nicht viel Zeit.
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Sign up to join this communityAs RHa mentioned, the conjugation of the verb depends on the subject. The subject is in the nominative case. Uns is the dative or accusative form of wir (in general, in this sentence it's dative), as such it cannot be the subject.
This leaves Zeit. Since Zeit is in singular, we need the third person singular conjugation of bleiben.
This becomes more obvious by rearranging the sentence:
Viel Zeit bleibt uns nicht.
Whether the verb is singular or plural depends on the subject.
The subject here is Zeit, which is singular. Therefore, it is bleibt, not bleiben. Uns is the (dative) object.
The word "uns" is clearly a dative object in this sentence, which has some people here misled that "Zeit" is the subject. The answer by infinitezero reasons that the sentence can be rearranged to
Viel Zeit bleibt uns nicht.
However, this rearrangement is an illegal operation in this context, because it swaps the roles of subject and objects! This is why "Zeit" becomes subject is this rearranged sentence. Hence, infinitezero's answer is incorrect: it is not "Zeit" that determines the form of "bleiben".
In the original
Uns bleibt nicht viel Zeit.
the word "Zeit" is an accusative object, as also hinted at by the position at the end of the sentence. The subject, in fact, is not visible, because it is omitted for convenience of speaking (note the discussed sentence is colloquial). The full sentence would be
Es bleibt uns nicht viel Zeit.
Here, it becomes obvious what is subject, and why the verb goes as "bleibt". "Bleiben", used with this meaning, is called an "unpersonal" verb in german grammar (i.e. cannot be used with first or second person pronouns, neither in plural: "Ich bleibe nicht viel Zeit." is nonsense), and correspondingly "es" is an unpersonal pronoun, whose omittance in colloquial speech in not uncommon.