Appears in collection : Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Notes: https://nextcloud.ihes.fr/index.php/s/gwxKFPnX5xTzmXS This is a joint work with G. Garkusha. In the talk I will discuss the construction of fibrant replacements for spectra consisting of Thom spaces (suspension spectra of varieties and algebraic cobordism ??? being the motivating examples) that uses the theory of framed correspondences. As a consequence we get a description of the infinite loop space of ??? in terms of Hilbert schemes.