On Voevodsky's algebraic K-theory spectrum BGL

Details On Voevodsky's algebraic K-theory spectrum BGL On Voevodsky's algebraic K-theory spectrum BGL

2007-09-25

arxiv.org/abs/0709.3905v2

Mathematics

Algebraic Geometry

LaTeX, 49 pages, uses XY-pic. Several changes. To appear in: The Abel symposium 2007

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On Voevodsky's algebraic K-theory spectrum BGL does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Voevodsky's algebraic K-theory spectrum BGL, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Voevodsky's algebraic K-theory spectrum BGL will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-626169