Bachmann, Tom and Hoyois, Marc (2021) Norms in motivic homotopy theory. ASTERISQUE (425). V. ISSN 0303-1179, 2492-5926
Full text not available from this repository. (Request a copy)Abstract
If f : S' -> S is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor f(circle times) : H.(S') -> H.(S), where H.(S) is the pointed unstable motivic homotopy category over S. If f is finite etale, we show that it stabilizes to a functor f(circle times) : SH (S') -> SH (S), where SH (S) is the P-1-stable motivic homotopy category over S. Using these norm functors, we define the notion of a normed motivic spectrum, which is an enhancement of a motivic E-infinity-ring spectrum. The main content of this text is a detailed study of the norm functors and of normed motivic spectra, and the construction of examples. In particular: we investigate the interaction of norms with Grothendieck's Galois theory, with Betti realization, and with Voevodsky's slice filtration; we prove that the norm functors categorify Rost's multiplicative transfers on Grothendieck-Witt rings; and we construct normed spectrum structures on the motivic cohomology spectrum HZ, the homotopy K-theory spectrum KGL, and the algebraic cobordism spectrum MGL. The normed spectrum structure on HZ is a common refinement of Fulton and MacPherson's mutliplicative transfers on Chow groups and of Voevodsky's power operations in motivic cohomology.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC K-THEORY; A(1)-HOMOTOPY THEORY; WEIL TRANSFER; OPERATIONS; COBORDISM; SPECTRA; DESCENT; OBJECTS; SLICES |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Aug 2022 05:24 |
| Last Modified: | 25 Aug 2022 05:24 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46928 |
Actions (login required)
 |
View Item |
