Bachmann, Tom and Yakerson, Maria (2020) Towards conservativity of G(m)-stabilization. GEOMETRY & TOPOLOGY, 24 (4). pp. 1969-2034. ISSN 1465-3060, 1364-0380
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 Apr 2021 08:14 |
| Last Modified: | 06 Apr 2021 08:14 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45389 |
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