Algebraic bordism spectra: Computations, filtrations, applications
Final Report Abstract
Within this research project Ahina Nandy proved that the canonical map MSL ∧ P∞ → MGL ∧ P1 of algebraic bordism spectra is an equivalence in the Morel-Voevodsky motivic stable homotopy category over any base scheme. As a rough idea of its plausibility: On the right hand side you find quadratic matrices with invertible determinant, on the left hand side you find quadratic matrices with determinant one, while P∞ as the classifying space of invertible numbers “remembers” the determinant. The corresponding topological result of Conner and Floyd then follows by complex realization. Proving the equivalence required numerous results from homotopy theory. The equivalence itself produces new results on slices and homotopy modules of MSL. Further results in connection with algebraic bordism spectra are the solution of Suslin’s conjecture regarding the relation of Quillen K-theory and Milnor K-theory in degree 4; both theories are suitable quotients of algebraic bordism spectra. A manuscript submitted for publication solves a version of Adams’ conjecture on spherical bundles obtained from Adams operations on vector bundles over regular varieties.
