Document Type
Article
Publication Date
12-1-2025
Abstract
We prove that Real topological Hochschild homology can be characterized as the norm from the cyclic group of order 2 to the orthogonal group O(2). From this perspective, we then prove a multiplicative double coset formula for the restriction of this norm to dihedral groups of order 2m. This informs our new definition of Real Hochschild homology of rings with anti-involution, which we show is the algebraic analogue of Real topological Hochschild homology. Using extra structure on Real Hochschild homology, we define a new theory of p-typical Witt vectors of rings with anti-involution. We end with an explicit computation of the degree zero D2m-Mackey functor homotopy groups of THR(Z_) for m odd. This uses a Tambara reciprocity formula for sums for general finite groups, which may be of independent interest.
Keywords
Mackey functors, real topological hochschild homology, rings with involution, Witt vectors
Language
English
Publication Title
Advances in Mathematics
Grant
DMS-1440140
Rights
© 2025 The Author(s). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/), which permits non-commercial copying and redistribution of the material in any medium or format, provided the original work is not changed in any way and is properly cited.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Angelini-Knoll, G., Gerhardt, T., & Hill, M. A. (2025). Real topological Hochschild homology via the norm and Real Witt vectors. Advances in Mathematics, 482, 110568. https://doi.org/10.1016/j.aim.2025.110568
Manuscript Version
Final Publisher Version