On the geometric fixedpoints of real topological cyclic homology
Abstract
We give a formula for the geometric fixedpoints spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to carry out computations in the fundamental examples of spherical grouprings, perfect $\mathbb{F}_p$algebras, and $2$torsion free rings with perfect modulo $2$ reduction. Our calculations agree with the normal Ltheory spectrum in the cases where the latter is known, as conjectured by Nikolaus.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.04891
 Bibcode:
 2021arXiv210604891D
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  KTheory and Homology
 EPrint:
 46 pages