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Explanation: I know the question has been closed but I think the asker was a little hasty in selecting an answer. The phrase "short application" isn't regularly used in English and doesn't conjure up any particular meaning, whereas Kurzbewerbung is commonly used in German to mean a cv accompanied by a covering letter, but without other detailed documentation. Depending on context, I'd recommending translating it by something like sending in ones c.v.
Eine Kurzbewerbung beinhaltet nur Anschreiben und Lebenslauf. Vor allem bei einer Initiativbewerbungen gilt sie als eine Alternative zur ausführlichen Bewerbungsmappe.