Rigidity II: non-orientable case

Abstract

The following paper is devoted to the construction of transfer maps (Becker-Gottlieb transfers) for non-orientable cohomology theories on the category of smooth algebraic varieties. Since non-orientability makes obstruction to the existence of transfer structure, we define transfers for a specially constructed class of morphisms. Being rather small, this class is yet big enough for application purposes. As an application of the developed transfer technique we get the proof of rigidity theorem for all cohomology theories represented by T-spectra.