Borel isomorphism and absolute purity
arXiv:1902.02055
Abstract
We prove absolute purity for the rational motivic sphere spectrum. The main ingredient is the construction of an analogue of the Chern character, where algebraic K-theory is replaced by hermitian K-theory, and motivic cohomology by the plus and minus parts of the rational sphere spectrum. Another ingredient is absolute purity for hermitian K-theory.