Krieger, JoachimLuhrmann, Jonas2015-04-012015-04-012015-04-01201510.1007/s40818-015-0004-yhttps://infoscience.epfl.ch/handle/20.500.14299/112844We prove global regularity, scattering and a priori bounds for the energy critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge on (1+4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gerard profile decomposition [1] and a concentration compactness/rigidity argument by Kenig-Merle [5], following the method developed by the first author and Schlag [10] in the context of critical wave maps. This is a preliminary version of the final paper.text::journal::journal article::research article