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On Voevodsky's Algebraic K-Theory Spectrum
- Source :
- Algebraic Topology ISBN: 9783642011993
- Publication Year :
- 2009
- Publisher :
- Springer Berlin Heidelberg, 2009.
-
Abstract
- Under a certain normalization assumption we prove that the P1-spectrum BGL of Voevodsky which represents algebraic K-theory is unique over Spec.(Z). Following an idea of Voevodsky, we equip the P1-spectrum BGL with the structure of a commutative P1-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over Spec.(Z). For an arbitrary Noetherian scheme S of finite Krull dimension we pull this structure back to obtain a distinguished monoidal structure on BGL. This monoidal structure is relevant for our proof of the motivic Conner–Floyd theorem (Panin et al., Invent Math 175:435–451, 2008). It has also been used to obtain a motivic version of Snaith’s theorem (Gepner and Snaith, arXiv:0712.2817v1 [math.AG]).
Details
- ISBN :
- 978-3-642-01199-3
- ISBNs :
- 9783642011993
- Database :
- OpenAIRE
- Journal :
- Algebraic Topology ISBN: 9783642011993
- Accession number :
- edsair.doi...........574d4ed9a43c3a505fd6a1d0af78c219