How to format a citation in the abstract
I was not able to find any mention of references in the abstracts in APA, MLA, Chicago, ASA (both statistics and sociology). There is no indication of if they are allowed and if so, if new formatting is required. I have found a few style guides that do describe references in the abstract.

APS style says:


  References cited in the abstract must also be found in the Reference List, where the complete information for the reference is provided. However, in the abstract, these references are not cited by their reference number alone. Instead, the following form of citation is used: the entire author list with initials (in roman); the journal name (in italics); and the volume, page numbers, and year (in roman). The article title is omitted for the sake of brevity.


which is pretty thin in regards to a citation style

IEEE style says:


  Numbered reference citations are not allowed.


which might imply full text citations are allowed like APS, but it goes on to say


  The abstract must be self-contained, without abbreviations, footnotes, or references. It should be a microcosm of the full article. 


AMS style seems to be the most complete:


  The abstract needs to be edited to
  remove
  or
  rewrite
  reference citations.
  Rewrite reference citations by placing the following information within
  brackets at the callout point. For journal article references, insert (in
  all lightface roman text) the journal abbreviation, volume, year, and
  page numbers, but not the article title. For book references, insert the
  title, publisher, location of publisher, and year. Only
  book titles
  appear
  in italics


it then gives three examples (article, book, and what looks like a book chapter).