We establish a general “affine representability” result in -homotopy theory over a general base. We apply this result to obtain representability results for vector bundles in -homotopy theory. Our results simplify and significantly generalize Morel’s -representability theorem for vector bundles.
Aravind Asok. Marc Hoyois. Matthias Wendt. "Affine representability results in -homotopy theory, I: Vector bundles." Duke Math. J. 166 (10) 1923 - 1953, 15 July 2017. https://doi.org/10.1215/00127094-0000014X