Corrigendum to “Symplectic and orthogonal $K$-groups of the integers”

Schlichting, Marco

doi:10.5802/crmath.606

Erratum - Théorie des nombres

Corrigendum to “Symplectic and orthogonal

K

-groups of the integers”
[Corrigendum à «

K

-groupes symplectiques et orthogonaux de l’anneau des entiers »]

Schlichting, Marco ¹

¹Marco Schlichting, Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK

Comptes Rendus. Mathématique, Tome 362 (2024) no. G3, pp. 307-308

corrige Symplectic and orthogonal K-groups of the integers
[K-groupes symplectiques et orthogonaux de l'anneau des entiers]

Abstract (VO)
Résumé

The action of the duality functor on the odd torsion of $K_{n} (ℤ)$ was stated incorrectly in [3], in half of the cases, and lead to incorrect formulas for the odd primary torsion of $π_{n} B Sp {(ℤ)}^{+}$ and $π_{n} B O_{\infty, \infty} {(ℤ)}^{+}$ .

L’action du foncteur de dualité sur la torsion impaire de $K_{n} (ℤ)$ était énoncé incorrectement dans [3], dans la moitié des cas, et a conduit à des formules incorrectes pour la torsion primaire impaire de $π_{n} B Sp {(ℤ)}^{+}$ et $π_{n} B O_{\infty, \infty} {(ℤ)}^{+}$ .

Reçu le : 2023-11-06
Accepté le : 2024-01-07
Publié le : 2024-05-02

DOI : 10.5802/crmath.606

Affiliations des auteurs :

Schlichting, Marco ¹

¹ Marco Schlichting, Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Corrigendum to {{\textquotedblleft}Symplectic} and orthogonal $K$-groups of the integers{\textquotedblright}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {307--308},
     year = {2024},
     publisher = {Acad\'emie des sciences, Paris},
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     number = {G3},
     doi = {10.5802/crmath.606},
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     url = {https://www.numdam.org/articles/10.5802/crmath.606/}
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Schlichting, Marco. Corrigendum to “Symplectic and orthogonal $K$-groups of the integers”. Comptes Rendus. Mathématique, Tome 362 (2024) no. G3, pp. 307-308. doi: 10.5802/crmath.606

Bibliographie
Cité par

[1] Calmès, Baptiste; Dotto, Emanuele; Harpaz, Yonatan; Hebestreit, Fabian; Land, Markus; Moi, Kristian; Nardin, Denis; Nikolaus, Thomas; Steimle, Wolfgang Hermitian $K$ -theory for stable $\infty$ -categories, Part III: Grothendieck-Witt groups of rings (2020) (https://arxiv.org/abs/2009.07225)

[2] Karoubi, Max Bott periodicity in topological, algebraic and Hermitian $K$ -theory, Handbook of $K$ -theory. Vol. 1, 2, Springer, 2005, pp. 111-137 | Zbl | DOI

[3] Schlichting, Marco Symplectic and orthogonal $K$ -groups of the integers, C. R. Math. Acad. Sci. Paris, Volume 357 (2019) no. 8, pp. 686-690 | DOI | MR | Numdam

[4] Weibel, Charles Algebraic $K$ -theory of rings of integers in local and global fields, Handbook of $K$ -theory. Vol. 1, 2, Springer, 2005, pp. 139-190 | DOI

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