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Witt vectors, polynomial maps, and real topological Hochschild homology
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Dotto, Emanuele, Moi, Kristian and Patchkoria, Irakli (2022) Witt vectors, polynomial maps, and real topological Hochschild homology. Annales Scientifiques de l'Ecole Normale Superieure, 55 (2). pp. 473-535. doi:10.24033/asens.2500 ISSN 0012-9593.
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WRAP-Witt-vectors-polynomial-maps-real-topological-Hochschild-homology-Dotto-2020.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (1195Kb) |
Official URL: https://doi.org/10.24033/asens.2500
Abstract
We show that various flavours of Witt vectors are functorial with respect to multiplicative polynomial laws of finite degree. We then deduce that the p-typical Witt vectors are functorial in multiplicative polynomial \textit{maps} of degree at most p−1. This extra functoriality allows us to extend the p-typical Witt vectors functor from commutative rings to Z/2 Tambara functors, for odd primes p. We use these Witt vectors for Tambara functors to describe the components of the dihedral fixed-points of the real topological Hochschild homology spectrum at odd primes.
On prouve que différents types de vecteurs de Witt sont fonctoriels en lois polynôme de degré fini. On en déduit que les vecteurs de Witt p-typiques sont fonctoriels en applications polynôme de degré au plus p−1. Cette fonctorialité nous permet d'étendre les vecteurs de Witt p-typiques des anneaux commutatifs aux foncteurs de Tambara pour le group Z/2, quand p est un nombre premier impair. On utilise ces vecteurs de Witt pour décrire les composantes des points-fixes diédraux de l'homologie de Hochschild topologique réelle aux premiers impairs.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Alternative Title: | Vecteurs de Witt, lois polynôme, et homologie de Hochschild topologique réelle | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Annales Scientifiques de l'Ecole Normale Superieure | ||||||
| Publisher: | Societe Mathematique de France | ||||||
| ISSN: | 0012-9593 | ||||||
| Official Date: | 13 March 2022 | ||||||
| Dates: |
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| Volume: | 55 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 473-535 | ||||||
| DOI: | 10.24033/asens.2500 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © 2022 Société Mathématique de France, Paris | ||||||
| Date of first compliant deposit: | 9 October 2020 | ||||||
| Related URLs: | |||||||
| Open Access Version: |
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