Abstract :
Letp be any prime. We consider Bo¨kstedtʹs topological refinementK(the ring of integers) → T(the ring of integers) = THH(the ring of integers)of the Dennis trace map from algebraicK-theory of the integers to topological Hochschild homology of the integers. This trace map is shown to induce a surjection on homotopy in degree2p − 1, onto the firstP-torsion in the target. Furthermore, Bo¨kstedtʹs map factors through theS1-homotopy fixed pointsT(the ring of integers)hS1 ofT(the ring of integers), and it is shown that the firstp-torsion element in degree2p − 3 of the stable homotopy groups of spheres is detected in the homotopy ofT(the ring of integers)hS1. Both results are due to Bo¨kstedt, but have remained unpublished.
