Trace maps from the algebraicK-theory of the integers (after Marcel Bo¨kstedt)
✍ Scribed by John Rognes
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 544 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0022-4049
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✦ Synopsis
Let p be any prime. We consider Biikstedt's topological refinement K(Z) -+ T(Z) = THH(Z) of the Dennis trace map from algebraic K-theory of the integers to topological Hochschild homology of the integers. This trace map is shown to induce a smjection on homotopy in degree 2p -1, onto the first p-torsion in the target. Furthermore, Biikstedt's map factors through the S' -homotopy fixed points I"( Z)hS' of T(Z), and it is shown that the first p-torsion element in degree 2p -3 of the stable homotopy groups of spheres is detected in the homotopy of T(Z)hS'. Both results are due to Biikstedt, but have remained unpublished. @ 1998 Elsevier Science B.V.