On Voevodsky's algebraic K-theory spectrum BGL
| dc.creator | Panin, I. | |
| dc.creator | Pimenov, K. | |
| dc.creator | Röndigs, O. | |
| dc.date | 2007-09-25 | |
| dc.date | 2008-10-27 | |
| dc.date.accessioned | 2026-07-07T10:12:50Z | |
| dc.date.available | 2026-07-07T10:12:50Z | |
| dc.description | Under a certain normalization assumption we prove that the $\Pro^1$-spectrum $\mathrm{BGL}$ of Voevodsky which represents algebraic $K$-theory is unique over $\Spec(\mathbb{Z})$. Following an idea of Voevodsky, we equip the $\Pro^1$-spectrum $\mathrm{BGL}$ with the structure of a commutative $\Pro^1$-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over $\Spec(\mathbb{Z})$. For an arbitrary Noetherian scheme $S$ of finite Krull dimension we pull this structure back to obtain a distinguished monoidal structure on $\mathrm{BGL}$. This monoidal structure is relevant for our proof of the motivic Conner-Floyd theorem. It has also been used by Gepner and Snaith to obtain a motivic version of Snaith's theorem. | |
| dc.description | LaTeX, 49 pages, uses XY-pic. Several changes. To appear in: The Abel symposium 2007 | |
| dc.identifier | https://arxiv.org/abs/0709.3905 | |
| dc.identifier | http://arxiv.org/abs/0709.3905 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172322 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 19E08; 55P43 | |
| dc.title | On Voevodsky's algebraic K-theory spectrum BGL | |
| dc.type | text |