Abstract
We study the interplay of the homotopy coniveau tower, the Rost-Schmid complex of a strictly homotopy invariant sheaf, and homotopy modules. For a strictly homotopy invariant sheaf M, smooth k-scheme X and q >= 0, we construct a new cycle complex C* (X, M, q) and we prove that in favorable cases, C * (X, M, q) is equivalent to the homotopy coniveau tower M-(q) (X). To do so we establish moving ...
Abstract
We study the interplay of the homotopy coniveau tower, the Rost-Schmid complex of a strictly homotopy invariant sheaf, and homotopy modules. For a strictly homotopy invariant sheaf M, smooth k-scheme X and q >= 0, we construct a new cycle complex C* (X, M, q) and we prove that in favorable cases, C * (X, M, q) is equivalent to the homotopy coniveau tower M-(q) (X). To do so we establish moving lemmas for the Rost-Schmid complex. As an application we deduce a cycle complex model for Milnor-Witt motivic cohomology. Furthermore we prove that if M-2 is a strictly homotopy invariant sheaf, then M-2 is a homotopy module. Finally we conjecture that for q > 0, (pi) under bar (0) (M-(q)) is a homotopy module, explain the significance of this conjecture for studying conservativity properties of the G(m)-stabilization functor SHS1 (k) -> SH(k), and provide some evidence for the conjecture.
Altmetric